Split volume for backups
You could absolutely do this. I've been using a setup like that for a while now and it works great.

What you want to do first is backup the files you have on the drive (backup the backup, haha) just so you can create two separate partitions on the drive. Formatting and partitioning the drive will make the data currently on the drive unavailable, so back up anything important!

Now, open up the Disk Utility application and select the external drive in the left pane of the window. Then click on the Partition button and here you can select any amount of partitions you wish to make. Unless you know you will need more later you could settle with two, one for Time Machine and one for important documents/files.



Continue by pressing the dropdown menu Volume Scheme and select 2 Partitions. You can now name each one and set their respective sizes, obviously a full Time Machine backup requires a fair amount of space so depending on how many backups you intend to have you might want to give this partition a bit of extra space.

You also want to specify which format (file system) to use for each partition. This is important if you intend to use the drive with other systems, for example Windows and Linux systems are not very fond of Mac OS Extended (Journaled) (aka. JHFS+). The Time Machine partition should be partitioned as Mac OS Extended (Journaled), but the other partition is up to you.

FAT32 (called DOS or MS-DOS sometimes) is the standard file system used by Windows (I believe), it can be used with Mac without any problems. The only drawback is that you can only store files that are less than 4Gb each, which is a pain if you handle large video files.

NTFS requires additional software for Macs to write, but it's (arguably) the most cross-compatible file system if you want to move files between different operating systems.



If you're only going to use the drive with a Mac, choose to format both partitions as Mac OS Extended (Journaled) and press Apply. This will create two new partitions that should work natively with any Mac.

Quick edit:
ExFAT can be an alternative to NTFS, depending on your Windows machine you might need additional software to read/write data to it.