cut, cutoff, be sharp
切 centers on the action of cutting or severing, and by extension the quality of being sharp enough to cut. The meanings 'cutoff' and 'be sharp' are natural applications of this core idea.
to cut; to cut through; to perform (surgery)
important; significant; serious; crucial
all; everything; entirety; the whole
end; finish; place to stop
appropriate; suitable; fitting; apt; proper; right; pertinent; relevant
piece; slice; strip; scrap
exchange; conversion; replacement; switching (to); switchover
to betray; to turn traitor (to); to double-cross; to go back on; to be unfaithful (to)
to break; to snap; to be cut; to split; to crack
kind; gentle; considerate; generous; friendly; nice
cutting; severance; section; amputation; disconnection
treachery; betrayal; perfidy
painful; heartrending; trying
unsuitable; inappropriate; improper
sold-out
stamp (postage)
ticket
reserving (for exclusive use); (full) booking; chartering; block reservation
end; close; finish; truncation; discontinuance; closure; cancellation; breaking off; aborting
deadline; closing; cut-off
to change; to switch; to change over (to); to renew
railway crossing; railroad crossing; train crossing; level crossing
partition; division; boundary; compartment
pause (in speech, writing, etc.); punctuation
切 combines 七 (originally a pictograph of cutting) and 刀 (knife), reinforcing the idea of cutting with a blade.
Seven 七 knives 刀 are lined up, all sharp and ready to cut. Imagine them slicing through a rope, severing it cleanly.
For セツ, picture a set of seven knives cutting in unison: set -> セツ, and the set of blades makes a sharp cut.