Chandio, for the way you are describing your set up, you will need to write a script to check the dates and delete them after they expire. You can do that in T-sql and incorporate it into your backup jobs, or you can write it as a shell script or some other language like python and then make it an operating system job.

Another option is to use a 3rd party program, such as RedGate sql backup, which will manage that for you.