Baby wipes work like a charm! I didn't have any stamp cleaner and I was stamping with both inks and acrylic paints. I grabbed a baby wipe and started wiping the stamp surface and it got it all off. And all the ink and paint that was on my hands too.
No harsh chemicals or special stamp cleaner needed, just a pack of baby wipes. Since one wipe can clean multiple stamp surfaces, you can put the wipe in a plastic bag to stay moist and use it again later!