to lick, to lap up, to burn up, to taste, to undergo, to underrate, to despise
舓 centers on the action of licking or lapping up, often with the tongue. The extended meanings of tasting, undergoing, underrating, or despising are less common and may be figurative uses of the licking idea, but they do not form a single clear conceptual center.
舓 combines 舌 (tongue) with 易, which likely contributes a phonetic element. The exact historical development is uncertain, but the tongue component clearly relates to licking.
The left side is a tongue 舌, and the right side 易 looks like a container being emptied. Picture a tongue lapping up the last drops from a bowl.
For シ, imagine a tongue licking a sheet of paper clean: sheet -> シ, and the tongue laps up every mark.