这段话到底表达什么？cut dowm 和 cut up 在这段话中的区别是什么？

A man was walking through a wood and he came across a woodcutter."what are you doing?" he asked. The woodcutter replied:"I'm going to cut this tree dowm."The next day he walked through the wood again. The woodcutter was standing next to a fallen tree,with lots of small pieces of wood in front of him."what are you doing?"he asked."I'm cutting this tree up," answered the woodcutter.
一个人穿过一片树林时碰到一个伐木者。“你在干什么呢”？他问道。那个伐木者回到说“我打算把这棵树砍倒。”第二天，他又穿过这片树林。那个伐木者站在一颗被砍倒的数的旁边，他的片面散落者很多碎的木片。“你在干嘛呢？”，他又问道。我要把这棵树切碎了”伐木者回到道

cut down 砍倒
cut up 切碎

cut down:砍倒

cut up: 切碎

前者是砍倒