Damage has already been assigned/dealt if the Slasher is regenerating due to combat damage.614.8. Regeneration is a destruction-replacement effect. The word “instead” doesn’t appear on the card
but is implicit in the definition of regeneration. “Regenerate [permanent]” means “The next time
[permanent] would be destroyed this turn, instead remove all damage marked on it and tap it. If it’s
an attacking or blocking creature, remove it from combat.” Abilities that trigger from damage being
dealt still trigger even if the permanent regenerates. See rule 701.11.