Tree radical on the left - the indexing semantic.
木 is the canonical tree pictograph (trunk, branches, roots).
杉 names the cedar / China fir, a specific tree species, so the radical does direct duty. Joins the tree-species family:
松 (pine),
柏 (cypress),
桃 (peach),
柳 (willow) - each with
木 on the left labeling the species.