The percentage of chance a Tree Ent will spawn when a tree is chopped down

Whenever you cut down a tree there is a small chance (larger at night) that a nearby tree will turn into one of these, some call them an "Optimus Pine".

Also, burning trees down will increase the chance of waking it up.

There are several popular strategies to deal with them:

• Lay a campfire and kite the monster over it to set it on fire.
• There is a bug where if you use a tent to change your skin it will stop chasing you.
• Get a pig man to attack it and it will stop chasing you.
• Kite it to a swamp and have it kill tentacles for you until it dies.
• Plant several pine cones between you and the Optimus Pine, it will eventually settle down and turn back into a tree.

I have only killed one once, and if I recall correctly it dropped logs and pine cones. It didn't drop anything special.

Stumps do not regrow, your only option is to plant pine cones to replace them. If left they will simply remain as an obstacle on the map until you dig them up with a shovel or burn them.