1962 Avalon Hill's Waterloo game
Soaking off was a term used when resolving combat during the play of the Avalon Hill game Waterloo. If you had a stack of units in a battle, or two stacks, you could assign some units to "soak off" a sacrificial attack (and likely be destroyed/removed from play) so that the rest of your units would more likely be successful in their attack against the rest of the enemy units.
It was a gamification of the military principle of "economy of force / mass at the point of decision."
That term seems to have migrated into RPGs. No surprise, given D&D's emergence (as the first RPG) out of the wargamer hobby.
Similarly, a sponge soaks up water/liquid when one is trying to dry up a wet surface, so to "soak" and to "absorb" mean roughly the same thing.
While I first learned this term in 1971, when I learned how to play Waterloo from a friend, the game was published in 1962.