You can choose which files and folder Time Machine backs up. When an existing device reports that it’s full, that’s one solution.
As the amount of files you have stored on you Mac increases, you may find that your back up harddrive isn't big enough for your Time Machine updates.
What do I do when Time Machine says the drive is full?
When your Time Machine drive is almost full, you’ll see a warning pop-up telling you. You should only see this once though as Time Machine is designed to do its own house-keeping.
Under normal circumstances - and given a backup disk or partition at least twice as large as the source drive -Time Machine begins delete old backups to make room.
But, there are times when it gets confused or is configured in such a way that you’ll get messages telling you your backup disk is full or Time Machine can no longer back-up. Here’s how to deal with those.
If you get a message saying Time Machine is full, it should be accompanied by an explanation telling you that it has deleted some old back-ups. It’s confusing, because it means that your backup disk is actually no longer full... You can turn off the notification by going to Time Machine’s Preferences and turning off back-up removal notification.
Your Time Machine will report that it’s full if you try to perform a full back-up larger than the existing capacity.
In some, fairly rare circumstances Time Machine will complain that the backup is too large, with the legend “Time Machine couldn’t complete the backup to ‘yourdrivehere’”.
If that happens, the backup drive really is too full. Time Machine will, by that stage, have attempted to jettison every room in the TARDIS, except the most recent backup.
There are a couple of things you can try. You can start over by erasing the current Time Machine drive using Disk Utility and doing a full backup to the freshly formatted drive. If the prospect of dual drive failure worries you, look at what Time Machine is backing up and exclude files and folders that it doesn’t need to add. There’s another solution, but it’s a potentially expensive one - and that’s to buy another external drive.