A sawmill assembly comprising a bed, a carriage and a tilting device. The bed has a pair of substantially parallel rails that define a first plane, a first axis perpendicular to the first plane, and a second plane perpendicular to both the first plane and a longitudinal axis of the rails. The carriage is movably supported along the rails. The tilting device allows a user to adjust a tilt angle of the carriage in the second plane, relative to the first axis. Also disclosed are methods of adjusting a blade angle of the sawmill assembly, and methods of cutting a tapered piece from a workpiece material.