For example, the trap card "Solemn Warning" has an effect that negates the activation of a monster effect and destroys that monster. If "Solemn Warning" is destroyed, its effect is not negated and the monster is still destroyed.
On the other hand, the trap card "Mirror Force" has an effect that destroys all face-up monsters on the field. If "Mirror Force" is destroyed, its effect is negated and no monsters are destroyed.
So, whether or not the effect of a trap card is negated if the card is destroyed depends on the specific card in question.