Can I cut into concrete floor in kitchen?
Yes, of course you can cut a trench through your concrete floor.

Be sure that you locate any existing wires or pipes that are in the path of the cut. A concrete saw with water will keep the dust to a minimum. Using a wet/dry vac to immediately suck up the water/dust will also help.  Be sure to seal off the space as best you can with plastic sheeting to keep the concrete dust out of the rest of the house.

You will likely want to dig below the concrete to make a space for the new pipe and then back fill to the level of the bottom of the concrete with sand or pea gravel.  Finally fill the cut with concrete and trowel it level with the uncut part.

Is it a lot of work?  Sure, but there is often no other way.