dispose, manage, deal with, sentence, condemn, act, behave, place
処 centers on taking action toward a situation: disposing of something, managing or dealing with a matter, and by extension, the place where such action occurs. The sense of sentencing or condemning is a specific application of dealing with someone's fate.
処 is the modern simplified form of 處. The older form combines 虍 (tiger) with 処, which likely contributed the sound and the idea of a place to sit or stop. The modern form retains the core shape but simplifies the upper element.
The outside 夂 looks like a person walking, and the inside 几 resembles a low table. Picture someone walking to a table to deal with paperwork, managing affairs at that place.
For ショ, imagine a show manager dealing with backstage chaos: show -> ショ, and the manager disposes of problems at the venue.
where; what place
processing; dealing with; treatment; disposition; disposal
disposal; throwing away; selling off
dealing with; coping with
execution
virgin (usu. female); maiden
measure; step; dealing with
restaurant; specialist
prescription (of medicine); formula
punishment; penalty
prescription
data processing; information processing
treatment (of a person); dealing with
aim; goal
to manage; to deal with; to cope with
dwelling; house; home; residence; abode; habitat
somehow; for some reason; in some way; vaguely
to manage; to deal with; to cope with
provisional disposition; temporary injunction
where; whereabouts