mow, cut grass, subdue
乂 centers on cutting down or controlling: mowing grass, cutting vegetation, and by extension subduing or bringing something under control.
乂 is an ancient pictograph of a cutting tool or scythe, representing the action of mowing or cutting down. The modern form retains the crossed-blade shape.
The two crossed strokes look like the blades of a scythe or shears, cutting through grass. That cutting action extends to subduing or bringing something under control.
For ガイ, imagine a guy mowing a field with a scythe: guy -> ガイ, and the crossed blades cut the grass.