Managing files when out of disk space on the server can cause an adminstrator to stress out. But if you have another...
server/workstation with free disk space, you can write a command file to perform a huge amount of file transfer. Xcopy is a very helpful tool for that procedure, and it will also create a respective directory in the new machine's folder.
"xcopy ServerAShare1Folder1* ServerBShare2Folder1 /I".
You can actually map a network driver as well. The /I switch at the end will assume that the destination "Folder1" is a folder name to be created if it doesn't exist.
Once you copy all of the files, you can run another command file to delete all of the transferred files by using:
"del ServerAShareAFolder1* /Q"
Switch /Q will not prompt for confirmation (i.e. quiet mode).
This should give you quite a lot of free space.