Typical mitre saws will not cut sharper than 50 degrees. They are limited by design and the fact that most commonly used mitre presets stop at 45 degrees. This doesn't mean that you can't cut a 60 degree angle. You can apply a trick that woodworkers use to cut extreme angles by adding a wedge behind the workpiece. A wedge deviates the degree of angle away from the fence, adding the necessary clearance needed to cross cut a 60 degree angle. Cross-cutting is cutting wood perpendicular to the grain.
Swing the mitre saw blade all the way to the left side, completely past the 45- degree preset until the blade will not go any farther.
Draw a 60-degree angle across a scrap board using a protractor and a pencil. Set the board on the mitre saw with angle that you drew directly under the blade. The long end of the board should be extended out on the left side of the blade.
Pull the saw blade down. Do not turn on the saw. Visually align the blade with the angle that you drew. They will not align.
Tap a wedge between the board and the mitre saw fence on the far left side of the mitre saw fence with a hammer. Keep looking at the alignment point of the saw blade and angle that you drew.
Tap the wedge as you watch the board begin to angle away from the fence. The angle that you drew on the board will begin to align with the blade as you tap the wedge. When the angle on the board aligns with the saw blade, stop tapping.
Hold the board tight against the fence with one hand, trapping the wedge in place and holding the board steady. Pull the trigger on the saw, bring the blade down and cross cut the 60-degree angle on the board.
If you're not sure about the angle, check it with the protractor. If it's not perfect, trim it again.
Always wear safety glasses. If the small cut-off piece goes behind the blade, hold the saw down all the way. Let go of the trigger. When the saw slows down and stops, let it return to its upright position. This prevents the small piece from kicking back out.