The battle can go either way
Triggers will not instantly kill a Mantis. It really depends on the species of trigger and mantis. I would not house them together regardless, because someone will get hurt.
The small mantis that are generally available...sure they won't fare well with a trigger (Or a puffer, for that matter)
I wouldn't want to be a triggerfish in a tank with a full grown
O. scyllarus.
Likewise, an adult L. maculata (An extreme example, but still...) eats fish...an 18" mantis is capable of killing and eating any trigger comercially available with little problem.
Even a small mantis is capable of doing life threatening damage to a triggerfish. Haplochlaena (Over on Grimreefers) posted about a small mantis that smashed one of his eels (It may have been a friend's, or a lab animal, I am not sure) in the face. The eel ended up with a broken mouth/teeth for his trouble/inquisitiveness.
-Ron