Right now the trunk and the branches on the tree is one mesh. I need to separate out all the branches into independent meshes as well as the tree trunk.
A model can consist of one or multiple objects, and one object can consist of one or multiple meshes (with mesh type objects). Objects in object mode and meshes in edit mode.
Y to split selection from unselected, V to rip an edge to the direction of the mouse cursor. P for separate menu, which separates geometry to its own object.