There are multiple instances in the Southern Campaigns in the Carolinas and Georgia of troops refusing quarter to surrendered or wounded enemy. Many of these were in retaliation for actions from Loyalist militia or other British troops. The Southern Campaign was unique in that it pitted colonists loyal to the King against Whigs fighting for an American republic, so opposite sides could quite literally be neighbors. A few specific instances would be the lack of quarter given by American militia to Loyalists after the Battle of Kings Mountain, where Patrick Ferguson, the commander of Loyalist forces, had his body urinated on after his death. Another example is Patriot horsemen riding down unarmed Loyalists after the Battle of Huck's Defeat, in upstate South Carolina. There are multiple instances of houses being burned, crops torched, etc. from both sides of the conflict.

If you're interested in the topic of the Revolution in the South, I'd recommend Partisans and Redcoats by Walter Edgar. It's well researched and covers the topic of atrocities on both sides in much more detail.