First tone 杈 is a forked wooden tool for moving hay or straw - concrete object. Don't confuse it with falling-tone 杈, the natural fork of a growing branch.
Left is the tree radical 木, placing the character among trees and timber. It tells you the splitting being described is in wood - where a branch divides off the trunk.
Right is 叉, a hand with a crossing stroke - both the sound and a strong meaning hint: a fork shape. Wood plus fork gives the branching point of a tree.
