You have to look at the Tree with an axe and hit it. if the Tree is fully grown you will see that you get Planks and thatch in your inventory when the tree is choped down coconuts will drop down. Cropplots are used to Grow potatos.(btw. If you hit smth. with an axe and a circle fills around your crosshair it means that you are destroing a part of your raft.
Are you hitting the frame around the tree? It shouldn't produce a circle, just a hitting effect and sound effect (and it will also give you items). If it shows the circle, you're doing it wrong. Try aim at the tree itself, not the surrounding area.