braid, cut
搓 centers on twisting or working fibers together: braiding strands into a cord, or cutting by a twisting motion. The two meanings connect through the idea of manipulating flexible material with the hands.
搓 combines 扌 (hand) with 差, which likely contributes the sound and may relate to the idea of crossing or interweaving strands. The exact historical development is uncertain.
The hand radical 扌 beside 差 suggests hands working on something that crosses or intertwines. Picture fingers braiding strands together, or twisting to cut a cord.
For サ, imagine braiding strands of silk (サ is the first syllable of さくら, cherry blossom, but here think of the sound 'sa' as in 'satin'). As you braid, you whisper 'sa, sa' with each twist.