In Campaign mode, a Savage Brute spawns on waves 5, 7, 10, 13 and 14. On Steam, it spawns on wave 4, too.
A Savage Brute always spawns in the westernmost hut in the village, carrying a damsel whom he intends to feed to the volcano. He will then proceed to the volcano, occasionally taking brief breaks. When he reaches the crater, he will throw the damsel into the lava: the sacrifice somehow awakens the volcano, that then will fire several big fireballs at your soldiers, dealing 100 damages in an area of effect.
Savage Brutes are out of reach of most towers, though reinforcements and heroes can be placed in their path, and can kill them fairly easily. An Archmage Tower placed in the closest strategic point to the path, and aided by a Crossbow Fort with Falconer, can hit the Brute when he first spawns, dealing huge damage.
In Heroic Challenge mode, a Savage Brute spawns in every wave. In Iron Challenge mode, they do not spawn - the volcano activates on its own. (On Steam, a Savage Brute spawns at the beginning of Iron Challenge.)
Savage Brutes are actually very easy to kill with most heroes, having surprisingly low HP for an enemy of that size.