Question

how an insect excrete ?

Answer 1

The Malpighian tubule system is a type of excretory and osmoregulatory system found in some insects, myriapods, arachnids, and tardigrades.

The system consists of branching tubules extending from the alimentary canal that absorbs solutes, water, and wastes from the surrounding hemolymph. The wastes then are released from the organism in the form of solid nitrogenous compounds and calcium oxalate. The system is named after Marcello Malpighi, a seventeenth-century anatomist.

It is unclear as to whether the Malpighian tubules of arachnids and those of the Uniramia are homologous or the result of convergent evolution.

hope it proves to be fruitful.....

Answer 2

here is your answer......
they excrete with the help of Malpighian tubules
The main excretory organ of the insect is the Malpighian tubule. Insects contain anything from 2 to 150 or more Malpighian 
tubules depending on the genus. Malpighian tubules are tubular outgrowths of the gut. They typically develop as pouches 
emerging from the junction between the midgut and the hindgut, though there actual final position varies - they may be attached to 
the midgut, hindgut or the midgut-hindgut junction as is the case with our ant above.
hope it helps.......