Specific role can only change status (active/blocked) of any user
As I mentioned in the question,


  I would like to give permission to that role he can change status (active/blocked) without editing the other fields...


I've done it without giving permission (Administer users) to role ONE.

I had to do configurations between tree modules Flag, Views and Rules. I created new flag, get flag in views using relationship and the add two simple rules. That's all

Let me post the answer, may be someone will need in the future.


Above mentioned three modules should be enabled with their UIs.


Creating Flag


Go to /admin/structure/flags/add, create a new flag and choose User as Flag Type, example 
After saving the Flag Type, fill next form like this, you may choose options as you like.


Creating Views


Now, create a views page/block as you like with showing Users category and your all fields you want to show and add a Relationship for the flag you just created (in my case it was "Block User").
Now, add a new field as Flag link in the views and add relationship if its already not and choose settings
Save the views


Creating Rule

We have to add to rules one for block the user and other for activate the user.

Block User


Add a new Rule /admin/config/workflow/rules/reaction/add and choose event "A user has been flagged, under Block User" and save
Add a condition using "Data comparison" and continue
Add value in data selector for flagged-user:status and continue
On next form, choose value as active and save
Now, add an action with Block User action and continue and add choose data selector for flagging-user and save


Activate User

There are same steps to activate users using rules. You just only to change event as "A user has been unflagged, under Block User", check the status as blocked instead of active and finally add action Unblock User instead of Block user.

All done...

Now, go to view the views you just created check if it works.

I hope it'll help someone.