Just like slicing with Simpler, Sampler doesn't "cut up" audio so much as assign a bunch of start and end points to a single audio file. While Simpler handles this with pads in a Drum Rack, Sampler assigns samples to note "zones" which you can take advantage of by doing some quick batch file processing.

Open up the Zones editor, select all, right click, and choose “Crop Sample” from the context menu. This will very satisfyingly crop all of the slices defined by the device to unique audio files.