Give the lumberjack the following tools to cut down a tree:

Round 1: Saw
Round 2: Chain Saw
Round 3: Knife

Scribblenauts Remix 6-4 Cheats Hints gallery:
6-4-1-a: Help him do his job!
6-4-1-b: Give him something to chop down the tree.
6-4-1-c: Give the lumberjack an axe.