I am in the process of putting down a new tile flooring and would like to have an electrical outlet in the center of the room. Is it possible to run a new electrical line to the center of the room off an existing outlet? To do that does the concrete slab need to be cut out to lay the electric line? Any guidance would be greatly appreciated.

Unfortunately yes.

Since you will be cutting the floor, make sure that the "one" outlet is enough for you.
You may as well think about future needs since you are already committed to making a mess.