I usually find it impossible to
get a perpendicular cut on thick items - the blade always seems to wander
off on its own path on the underside.


The secret is to steer by twisting the saw along the axis of the blade, and
resist any temptation to apply sideways forces (like you would to steer a panel
saw).

(To be a bit technical, pushing sideways creates a bending moment on the blade
between the top of the surface and the saw and this causes the blade to, well,
bend).