I have a late 2009 iMac with a 1tb hard drive running Snow Leopard. Can I partion the hard drive and upgrade to Mountain Lion on one part and keep Snow Leopard on the other? If not, can I partition my external back-up drive that I use for Time Machine to do the same thing?
No. For that you need something like Parallels, though I am not certain it is designed for anything other than a Windows installation.
Using the solution you proposed requires you boot into the partition containing the OS X version you want. Use Startup Manager (hold an Option key while starting your Mac).
If you are really concerned obtain an external hard disk drive and install ML on it. You won't have to touch your iMac's hard disk.
A cheap way to do that is to find a PC that was discarded due to viruses or other frustrations, harvest its hard disk and return the rest to the trash. Buy a USB enclosure for the drive (about $20) and reformat it for OS X.