Let's make this example easy—say you're image to be split is 320 x 320px.
- Draw a slice that is 32 x 32.
- With the slice selected, hit ctrl + D nine times for a total of 10 slices.
- Go to the align palette (make sure the "to stage" button is clicked) and align to the top.
- Then use the distribute horizontally command from the same palette.
- Now select all 10 slices and ctrl + D to duplicate the row.
- Move the second row into position and repeat.
Now you can export slices and you'll have all the 32x32 images you need.
Quick 'n dirty: drag horizontal and vertical guidelines over your image every 32 pixels. Choose File > Export. In the Export dialogue window, choose Export Images only, and Slice Along Guides. Click the Save button.