are you using the seagate backup software?
Are you wanting the backups to stop completely or are you wanting it to stop backing up the external drive?
Depending on the backup software that you are using, When you configure the backups, You can choose the drive letters to back up so you can choose whatever partitions you want, but then there should be a place to designate how many backups to keep at any given time.
So lets say your C: is about 150gb of data being used, every backup will eat up 150gb so you will be able to run 6 backups and the 7th will fail unless you are deleting the backups. But if you tell it to only keep 3 instances of the backups, once your drives backup 3 times, the next backup will continue as normal but it will replace the oldest backup so at any given time, you will have your 3 latest backups, this would have you at 450gb leaving you ~550 for other data.