When taking a snapshot, previous snapshot files are not automatically deleted. You should remove old snapshots that are no longer needed.
The nodetool clearsnapshot command removes all existing snapshot files from the snapshot directory of each keyspace. You should make it part of your back-up process to clear old snapshots before taking a new one.
But if you delete first, then there is a window of time when no snapshot exists until the new one is created. And with a single snapshot there is no recovery further back than it.