to split apart, to break up, to open
拆 centers on forceful separation: splitting something apart, breaking it up, or prying it open. The given meanings all describe a single action of dividing or opening by force.
拆 combines 扌 (hand) with 斥, which likely contributes the sound and the idea of pushing away or separating. The exact historical development of 斥 within this character is uncertain.
The hand radical 扌 beside 斥 suggests a hand forcefully pushing something apart. Imagine a hand splitting a log by driving a wedge into it.
For タク, imagine a hand splitting a tacky piece of clay: tack -> タク, and the hand breaks it open.