how do i clear old backups from time machine to make more space

My 2TB Time Machine is nearly full. I am trying to back up a drive in a Mac Min that is starting to fail and wanted to do so on Time Machine. Unfortunately since my Time Machine is nearly full it will not back up drive without eliminating nearly all of the files on this Mini. I am okay overwriting the other backups already on the Time Machine but do not know how to force Time Machine to do so. Please any clues on how to make Time Machine overwrite other backups would be greatly appreciated.