exclude, division (x/3), remove, abolish, cancel, except
除 centers on taking something away or setting it apart: removing, excluding, canceling, or abolishing. The mathematical division sense is a specialized application of separating into parts.
除 combines ⻖ (mound, hill) with 余, which likely contributes the sound. The original meaning is associated with removing or clearing away, possibly from the idea of leveling a mound.
The mound radical ⻖ on the left and 余 on the right suggest a mound being leveled or taken away. Picture a hill being removed to make space, just as 除 means to exclude or abolish.
For ジョ, imagine a judge ordering the removal of an obstacle: judge -> ジョ, and the mound is cleared away.
cleaning; sweeping; dusting; scrubbing
to remove; to get rid of; to take away; to eliminate
termination (of a contract); cancellation; rescinding; rescission
deletion; elimination; erasure; striking out
exclusion; removal; elimination; clearing away; getting rid of
division
removal; getting rid of
exception; exclusion
extermination (of pests); eradication; stamping out (e.g. a social evil)
protection; repellent
exemption; exoneration; discharge
to remove; to deinstall; to take away; to set apart
cut off; cut out; ablation; resection; surgical removal
subtraction; deduction (e.g. of tax)
snow removal
striking off a name; dropping a name (from a list); expulsion; excommunication
military discharge
weeding
prevention (of plant disease and insect damage); (pest) control; extermination (of harmful insects)
insecticide; insect repellent