How can I separate some collections to another server?
Yes, it's possible. But after moving data to another server, your application must have mean to connect that server when it needs to read/write that DB.Collection.

It is possible even in sharded cluster, I have done that. In that case too, application must have mean to connect that "second" RS or Cluster.

You must give more information, if you need doable solution.

With https://github.com/mongodb-labs/mongo-connector you can easily replicate single/RS/Cluster to destination...