break, smash, crush, familiar, popular
摧 centers on forceful destruction: breaking, smashing, or crushing something. The less common senses of 'familiar' and 'popular' seem unrelated and may be rare or archaic; the main idea is violent breaking.
摧 combines 扌 (hand) with 崔, which likely contributes the sound and may suggest a high, imposing force. The character expresses breaking or crushing by hand or by overwhelming pressure.
The hand radical 扌 beside 崔 (a tall mountain-like shape) suggests a hand bringing down something massive, like smashing a rock from a cliff. Picture a hand crushing a towering structure.
For サイ, imagine a sigh of relief after you smash something frustrating: sigh -> サイ, and your hand delivers the crushing blow.
Tract for Destroying Heretical Views (Buddhist treatise by Myoe, ca. 1212 CE)