Q: What did the angry lumberjack say to the tree?
A: I have an axe to grind with you!
Explanation: Lumberjacks are people who work cutting down trees so that people can use wood to make things. Many years ago, lumberjacks would use a saw and/or an axe to cut down trees. (Hopefully they planted two new trees for each one cut down!) Before working with an axe, it is important to sharpen the axe. One way to sharpen the axe is to use a grinder.
“Have an axe to grind” with someone is an idiom. It means that you have a personal, maybe selfish reason for saying something, or that you have a complaint that you have to talk to someone about. Here are some examples from Linguee.com. (Linguee is one of my favorite sites for translating, by the way.)
This joke is funny because it plays with the idea of grinding an axe, both the literal idea of using an axe sharpened on a grinder to cut down a tree, and the figurative idea of the idiom have an axe to grind.
Here is one of the most famous fictional lumberjacks, Paul Bunyan, from 1958: