Just scanning-through the datasheet I don't see any way to stop playback or any way to start/restart anywhere other than the beginning.
When a HIGH-going transition is detected on this input pin,
a playback cycle begins. Playback continues until an End-of-Message (EOM) marker is
encountered or the end of the memory space is reached.
Conceptually, it's easy to make playback stutter with a computer (or maybe with a Raspberry Pi) but it would take fairly advanced speech recognition to find the beginnings of words to simulate the way a human stutters in a realistic way.
...that raises awareness for people with disabilities. They reached out to my school to make a "Stutter Box". The basic idea is for someone to record themselves speaking, then the devices plays the audio back but it makes them have a stutter.
Personally, I wouldn't be impressed by a screwed-up recording of myself.