The thing is that insects don't have lungs like mammals, birds, and reptiles. Consequently, the principle of producing sound from the mouth is extremely rare.
I'm unaware of any cases where an insect per se actually produces noise with its mouth; however, there is a moth caterpillar (Nessus sphinx hawkmoth larva) which produces a squeaking noise by forcing air in and out of its gut through its mouth when it is disturbed (Rosi-Denadai et al. 2018).
Source:
- Rosi-Denadai, Conrado A., Melanie L. Scallion, Craig G. Merrett, and Jayne E. Yack. "Vocalization in caterpillars: a novel sound-producing mechanism for insects." Journal of Experimental Biology 221, no. 4 (2018): jeb169466.