Hi & welcome to macProVideo forums :)
There are some third party plugins that can produce stuttering effects. For example check out Audio Damage's Replicant.
However, it may be easier to use editing tools in Logic to achieve the exact effect you want.
You can time stretch the audio region (Hold down Option and drag the right boundary of the region to do this).
Then slice up the region using the scissors or double clicking with the marquee tool. One way to slice a region into equal segments:
Use the Scissors tool and hold down Option and click at the first division or bar. Equal segments will then be cut in the region.
A lot of glitch artists do use plugins and many other simply cut, copy, paste, shorten/stretch a region to achieve this in the Arrange. It is a manual process but gives you a lot of control.
Hope that helps,