Windows Server Backup (WSB) was introduced with Server 2008. WSB uses automatic space and version management, so in theory there should be no need to manually clear old backups to make space for the new ones.  Of course the difference between theory and practice is that in theory there is no difference; in practice there is…

 You may one day notice that your WSB backups fail with error code 2155348010 (hex 0x8078002A) “One of the backup files could not be created”.  If you check the backup target disk you find there is little free space.  You can format the disk (losing all backups on it), buy a larger disk, or try deleting snapshots from the disk using Diskshadow.exe.

I usually assign a drive letter to the backup disk using the Disk Management MMC snap-in – this just makes it easier by referring to the target disk by drive letter (eg Q:\) rather than the volume GUID (eg \\?\Volume{47ba2efc-2db1-11e0-88f8-806e6f6e6963}\). 

Then run the command ‘diskshadow > delete shadows oldest Q:’ and check space on the disk.  Rinse and repeat as necessary.  That’s it.

Ref:Microsoft Storage Team Blog – Windows Server Backup automatic disk usage management