What is the easiest way to cut a 2 inch groove in concrete?
I'd try to go through the slab and then below it.  Most slabs are 6" thick with gravel underneath.

You can rent a concrete core drill for around $60 from home depot. Stick a hole in your slab.

Then you can use something called a 'sidewalk sleever' to tunnel under the slab.  Then install pipe (a little tricky due to the elbow, and fill your hole back up with gravel. 

The end result will be much prettier and do less damage to your slab.