Can a sword of life stealing steal more hp than the target has?


The entry for Sword of Life Stealing says: "When you attack a creature with this magic weapon and roll a 20 on the attack roll, that target takes an extra 10 necrotic damage if it isn’t a construct or an undead. You also gain 10 temporary hit points.

Note: According to the SRD, it is an extra 3d6 necrotic damage."

However, my DM says that a Sword of Life Stealing inflicts its damage in a certain order on a natural 20: first the regular damage, then crit damage, THEN the necrotic damage…so if by that point the target has no more hp left to lose, I receive no temporary hp. Basically he said that the target "has no more life to steal".

I thought this was a bit of a strange interpretation. Is there an official ruling somewhere?