Store Mysql Index in separate .Ibd file?
In theory it's possible. What you call a table in InnoDB is a B+tree index named PRIMARY. The key in the PRIMARY index is the primary key field(s). 

All secondary indexes are B+tree indexes, too. The key would be the secondary index field(s). The value is the primary key.
(See my slides to get more details http://www.slideshare.net/akuzminsky/indexes-in-my-sql-aleksandr-kuzminsky-https-twindbcom?ref=https://twindb.com/efficient-use-of-indexes-in-mysql/)

Although logically the PRIMARY and secondary indexes are separate they're still stored in one .ibd file (that's assuming innodb_file_per_table=ON). There is no way to store them in separate files.