Doc,if you are looking at the same "manual" as I have for the sanitation hoses, tanks, etc, do yourself a favor and throw that crap away. It shows several different possibilities, none of which seem to pertain to much. Most confusing drawing I've ever seen, right next to the wiring diagram.
That pump you're looking at is likely called a macerator pump, and they are generally fairly reliable and simple. The bigger hose coming out the front of it should go to your holding tank, maybe being routed through a valve as previously suggested, and the smaller hose coming off of the side should run to a thru-hull valve, enabling you to pump it overboard. If the wires have been cut, it sounds kind of odd, as that is one system on the boat that I want to work. So in effect, all that pump is doing is pumping the tank, straight to the valve. I can not advise trying any "home remedies" for pumping it back out of the waste pipe that is located in the cockpit. It can be done in a few different ways, but you'll wish you had never attempted it.
Once you get the pump working, (try and not run it dry for too long, they don't like that), and the thru-hull open, keep pumping, and filling with fresh water from the topside until you get it rinsed out good. And then......the odyssey begins. Whole books have been written on the topic of keeping a system clean and smelling good. Vinegar, and Odorlos come to mind for de-fumigating it, and I'll leave that research to you. But in the end, this is one system, from the tank, head, hoses, and pump that will be best served by a burial at sea, in the same spot where bin-laden was kicked overboard, and replace it with new. If you have a wife, or girlfriend that comes on board with you, and you would like for them to return a second time, I urge you to consider this advice...