Index can not be disabled; you'll have to drop it.
> DROP INDEX index_name;
However, you can make it unusable:
> ALTER INDEX index_name UNUSABLE;
To bring it back, you'll have to rebuild it:
> ALTER INDEX index_name REBUILD;
If you mixed terms "index" and "constraint", well, constraints can be disabled (and enabled).
It is expected that performance will be degraded if you drop index. However, if it is about mass insert, then it is perhaps better to first drop all indexes, perform insert and, finally, create indexes because their presence might slow things down.