An oblique fastening apparatus includes first and second clamping units. The first clamping unit includes a first main body, a first guide member, a first clamping member, and a first oblique fastener passage extending through the first guide member and the first clamping member and having a first discharge section communicating with ambient atmosphere. The second clamping unit includes a second main body movable relative to the first main body, and a second clamping member. The first and second clamping members are configured to clamp a workpiece therebetween. A guide unit is provided to guide relative movement of the first and second main bodies.