Well that is the reference they claim to derive it from, yes. But that's no derivation, that's really just making stuff up. It's a very specific and narrow command, and part of the theme of prohibiting cruelty to animals. The commandment says nothing about mixing meat and dairy, it says not to cook a kid in the milk of its mother (which, yes, was apparently a widely practiced and deliberately cruel pagan rite practiced at the time.) If it was intended to prohibit mixing meat and dairy it would say so, there is no reason it could not have said that clearly if that was what was meant.
The Rabbinate 'interpretation' is based on Midrash, figurative leaps and flights of fancy, as well as the evolving needs of the Rabbinate itself (which strengthened its own power over the people by expanding the rules until they became impossible to follow.) But for a Karaite a valid interpretation of any passage must be consistent with the plain language and grammar of the passage, as well as its context, all of which plainly contradict the Rabbinate reading.
(As an aside, and no offense intended, the same reasoning leads to rejection of scriptural status for the 'New Testament' right along with the Talmud, both works deeply rooted in Midrash and both contradict the plain words of the Tanakh at one place or another.)