How can I separate some collections to another server? If my server disk is fulled, I want to move some collections to another server.

Is it possible?

Is there another way from sharded cluster implementation?
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...