As snubby suggests, I would go with a diversion cut. Depending on the slop from the lower side back to the drain, you might be able to get away with running it back towards the drain. Obviously, your cut would get deeper as you move back towards the drain. If however this would prove to be too much, I would simply make a diversion cut on the lower side, put in a sump crock, and drain the water out the back of the garage and not even worry about connecting it to the drain. This would be your easiest and cheapest option!

You can rent a good cement saw at a rental place. Not a chainsaw type saw but an actual walk behind saw with water attachment. This will give you the straightest cut and allow you to be a little more precise in your depth. You could also create a "V" cut in the concrete to a collection location (sump) and then put in a drain. Another option would be a trough cut whereas you creat a trough for the water to channel. You can cover it with grating. These cuts could also be performed with a quality angle grinder and a good diamond blade while following a red chalk line snapped on the floor. It would however take you considerable more time and require a bit more precision on the part of the operator.