bite
嚼 centers on the physical act of biting or chewing with the mouth.
嚼 combines 口 (mouth) with 爵, which likely contributes the sound and may relate to a drinking vessel, but the exact historical development is uncertain.
The mouth 口 beside 爵 suggests a mouth working on something tough, like biting into a ceremonial vessel.
For シャク, imagine biting into a shackle to break free: shack -> シャク, and your mouth 口 is doing the biting.