Most commonly when someone brings me a car or vehicle that is stuttering when accelerating it's caused by the fuel not getting to the fuel injectors fast enough or properly.
Usually the cause is as simple as replacing the fuel filter due to it being partially clogged and replacing the fuel filter usually solves the problem.
However sometimes I find the cause to be a bad fuel pump after doing a fuel pressure test and replacing the fuel pump helps the car run smooth again.
A car or vehicle can also sputter upon accelerating due to problems with the ignition system as well or bad spark plugs, bad ignition coils, bad spark plug wires etc.
I would have Autozone or a mechanic plug in a tester to the computer on the car and find out what could be causing the sputtering.