You mean they would (try to) destroy their enemies even if it meant their own assured destruction?
NO. More often told as frog and scorpion. They have to cross water, but the frog is unhappy as scorpions kill frogs. The scorpion points out that this would be silly as the scorpion would die too. The frog agrees and sure enough half way across the scorpion stings the frog. As they both die the frog asks the scorpion why?
the scorpion replies - I'm a scorpion, its what I do.
(its paraphrased & seriously annotated but you get the point.)
Mating for all of the arachnids is very tricky, the male has to be very careful to avoid getting eaten and in some species it is very common. However its not a universal truth and if it goes wrong the female can end up as lunch too. Scorpions also have rather 'interesting' mating habits for the same reasons.
I have never heard of any spider or scorpion 'playing' a la feline with its food. They have poisons, they don't need to bother.