How to grant super privilege to the user?
In a politically correct sense, what you just asked for is impossible. Why ?
The SUPER privilege is a global privilege, not a database level privilege.
When you created the user with
grant all privileges on db1.* to user1@'%' with grant option;

you populated the table mysql.user with user='user1' and host='%'. All other columns (global  privileges) were defaulted to 'N'. One of those columns is Super_priv. Here is the table:
mysql&gt; desc mysql.user;
+------------------------+-----------------------------------+------+-----+---------+-------+
| Field                  | Type                              | Null | Key | Default | Extra |
+------------------------+-----------------------------------+------+-----+---------+-------+
| Host                   | char(60)                          | NO   | PRI |         |       |
| User                   | char(16)                          | NO   | PRI |         |       |
| Password               | char(41)                          | NO   |     |         |       |
| Select_priv            | enum('N','Y')                     | NO   |     | N       |       |
| Insert_priv            | enum('N','Y')                     | NO   |     | N       |       |
| Update_priv            | enum('N','Y')                     | NO   |     | N       |       |
| Delete_priv            | enum('N','Y')                     | NO   |     | N       |       |
| Create_priv            | enum('N','Y')                     | NO   |     | N       |       |
| Drop_priv              | enum('N','Y')                     | NO   |     | N       |       |
| Reload_priv            | enum('N','Y')                     | NO   |     | N       |       |
| Shutdown_priv          | enum('N','Y')                     | NO   |     | N       |       |
| Process_priv           | enum('N','Y')                     | NO   |     | N       |       |
| File_priv              | enum('N','Y')                     | NO   |     | N       |       |
| Grant_priv             | enum('N','Y')                     | NO   |     | N       |       |
| References_priv        | enum('N','Y')                     | NO   |     | N       |       |
| Index_priv             | enum('N','Y')                     | NO   |     | N       |       |
| Alter_priv             | enum('N','Y')                     | NO   |     | N       |       |
| Show_db_priv           | enum('N','Y')                     | NO   |     | N       |       |
| Super_priv             | enum('N','Y')                     | NO   |     | N       |       |
| Create_tmp_table_priv  | enum('N','Y')                     | NO   |     | N       |       |
| Lock_tables_priv       | enum('N','Y')                     | NO   |     | N       |       |
| Execute_priv           | enum('N','Y')                     | NO   |     | N       |       |
| Repl_slave_priv        | enum('N','Y')                     | NO   |     | N       |       |
| Repl_client_priv       | enum('N','Y')                     | NO   |     | N       |       |
| Create_view_priv       | enum('N','Y')                     | NO   |     | N       |       |
| Show_view_priv         | enum('N','Y')                     | NO   |     | N       |       |
| Create_routine_priv    | enum('N','Y')                     | NO   |     | N       |       |
| Alter_routine_priv     | enum('N','Y')                     | NO   |     | N       |       |
| Create_user_priv       | enum('N','Y')                     | NO   |     | N       |       |
| Event_priv             | enum('N','Y')                     | NO   |     | N       |       |
| Trigger_priv           | enum('N','Y')                     | NO   |     | N       |       |
| Create_tablespace_priv | enum('N','Y')                     | NO   |     | N       |       |
| ssl_type               | enum('','ANY','X509','SPECIFIED') | NO   |     |         |       |
| ssl_cipher             | blob                              | NO   |     | NULL    |       |
| x509_issuer            | blob                              | NO   |     | NULL    |       |
| x509_subject           | blob                              | NO   |     | NULL    |       |
| max_questions          | int(11) unsigned                  | NO   |     | 0       |       |
| max_updates            | int(11) unsigned                  | NO   |     | 0       |       |
| max_connections        | int(11) unsigned                  | NO   |     | 0       |       |
| max_user_connections   | int(11) unsigned                  | NO   |     | 0       |       |
| plugin                 | char(64)                          | YES  |     |         |       |
| authentication_string  | text                              | YES  |     | NULL    |       |
| password_expired       | enum('N','Y')                     | NO   |     | N       |       |
+------------------------+-----------------------------------+------+-----+---------+-------+
43 rows in set (0.00 sec)

mysql&gt;

Super_priv appears right after Show_db_priv.
The database level privileges got populated into mysql.db. Here is it:
mysql&gt; desc mysql.db;
+-----------------------+---------------+------+-----+---------+-------+
| Field                 | Type          | Null | Key | Default | Extra |
+-----------------------+---------------+------+-----+---------+-------+
| Host                  | char(60)      | NO   | PRI |         |       |
| Db                    | char(64)      | NO   | PRI |         |       |
| User                  | char(16)      | NO   | PRI |         |       |
| Select_priv           | enum('N','Y') | NO   |     | N       |       |
| Insert_priv           | enum('N','Y') | NO   |     | N       |       |
| Update_priv           | enum('N','Y') | NO   |     | N       |       |
| Delete_priv           | enum('N','Y') | NO   |     | N       |       |
| Create_priv           | enum('N','Y') | NO   |     | N       |       |
| Drop_priv             | enum('N','Y') | NO   |     | N       |       |
| Grant_priv            | enum('N','Y') | NO   |     | N       |       |
| References_priv       | enum('N','Y') | NO   |     | N       |       |
| Index_priv            | enum('N','Y') | NO   |     | N       |       |
| Alter_priv            | enum('N','Y') | NO   |     | N       |       |
| Create_tmp_table_priv | enum('N','Y') | NO   |     | N       |       |
| Lock_tables_priv      | enum('N','Y') | NO   |     | N       |       |
| Create_view_priv      | enum('N','Y') | NO   |     | N       |       |
| Show_view_priv        | enum('N','Y') | NO   |     | N       |       |
| Create_routine_priv   | enum('N','Y') | NO   |     | N       |       |
| Alter_routine_priv    | enum('N','Y') | NO   |     | N       |       |
| Execute_priv          | enum('N','Y') | NO   |     | N       |       |
| Event_priv            | enum('N','Y') | NO   |     | N       |       |
| Trigger_priv          | enum('N','Y') | NO   |     | N       |       |
+-----------------------+---------------+------+-----+---------+-------+
22 rows in set (0.00 sec)

mysql&gt;

Notice that Super_priv does not exist in mysql.db.
To visualize this in pure SQL terms, login as user1 and run SHOW GRANTS; The output will have two lines:

GRANT USAGE ON *.* TO user1@'%' ...
GRANT ALL PRIVILEGES ON db1.* TO user1@'%' ...

There is a hack you can try but I normally would not recommend it.
STEP 01) Login to mysql as root@localhost (should have all privs)
STEP 02) Run this query
UPDATE mysql.user SET Super_Priv='Y' WHERE user='user1' AND host='%';

STEP 03) Run this query
FLUSH PRIVILEGES;

That theoretically should work. Then, user1 may work (I make no guarantees).
UPDATE 2014-12-19 15:24 EST
Metafaniel just asked

Great explanation, thanks. However if you do not reccomend that way to solve the problem, then what other way is the best one to gran a user this Super_priv?? Thanks! –  Metafaniel

Since a user with only DB access cannot have SUPER, the only thing one can do is change the DEFINER manually in the dump. The basic idea would be to mysqldump the routines alone to a text file. Then, edit the definer to user1@'%'. Then, you should be able to reload.

Oct 02, 2011 : Can mysqldump dump triggers and procedures?
Jul 25, 2011 : DROP PROCEDURE IF EXISTS not included in mysqldump
Jul 25, 2011 : Dump only the Stored Procedures in MySQL

Same Thing for Views

Mar 23, 2012 : MySQL Views Authorization
Jul 26, 2011 : Modify DEFINER on Many Views