That's the problem with TimeMachine it's only a rotational backup system and not permanent storage.
It's also saving things you don't want.
What you should rather look at is a bootable clone.
What you do is you take your external drive and format it 2 partitions Option GUID and OS X Extended journaled in Disk Utility.
One partition is the slightly larger than your internal boot drive, then you use Carbon Copy Cloner to image your internal boot drive to that partition (must be first one) and set CCC to maintain a pure clone (or it will save the states like TM does)
The clone is hold option/alt key bootable with a wired or built in keyboard.
Next you have the remaining space on that other partition to save files in a more permanent state.
Now I typically don't recommend putting all your backup eggs in one hardware basket because you might drop the thing and lose both, but if your careful and at the first chance you get buy another drive and make more backups then no problem.