Stomp means "to tread on," "to trample," "to step violently on or upon." As a verb, stamp has several meanings, including that of stomp: One can stamp (or stomp) a snake to death. One is more likely to refer to stomping horses or herds than to stamping horses or herds, but both adjectives are correct. In the senses of eliminating, getting rid of, and striking the ground with the human foot, stamp is preferred: "This action will stamp out slums." "In her anger, she stamped her foot on the floor."
Dictionary of problem words and expressions. Harry Shaw. 1975.