Poseidon's realm not your thing when it comes to office supplies? Then harness the almighty power of Mother Nature to cut your tape.

These vines are meant to grow out of your wall (be it apartment or cubicle) but may need some help with a few well-placed thumbtacks (or use the screwholes version to seriously mount that sucker to your wall).

~Thanks to Thingiverse User stateofkate for suggesting vines as being a potential tape-cutting entity~

Dual/Multi color options in the form of Part1 and Part2 or a straight single color option available.  
Like Tentacle Tape Dispenser, this is a great use for one of your old x-acto blades. But if you don't want to risk slicing a finger open, you could print out TapeBlade.stl for a sweet serrated cutting blade.

Modeled in Meshmixer - Successfully printed in dual PLA colors on a Flashforge Creator.