Tree radical on the left, the indexing component. Pictograph of a tree with branches and roots. It marks 杵 as a wooden tool — the pestle was carved from a single hardwood length — and groups it with other wooden utensils: 棒 stick, 杠 pole, 桨 oar, 杆 rod.
Right side 午 wǔ supplies the sound with a regular shift wǔ → chǔ (an old initial alternation). 午 itself was originally a pictograph of a pestle, and 杵 added 木 to mark it as the wooden implement — picture and meaning aligned from the start.
