Skirting is too wide for mitre box
Use the mitre box to guide the saw but make the cut outside the box.


Clamp the box to a table.
Place a board at least as thick as the bottom of the mitre box behind the box. Clamp it to the table or just hold it against the box while working.
Place the material to be cut on the board and hold it against the
mitre box. 
Use a saw long enough to reach across the mitre box + work + cutting
stroke.


EDIT: This is the correct answer to the wrong question. OP is asking about cutting material that is too high for the mitre box; this answer is good for material that is too wide for the box. 

So the analogue of my technique for op's too-high material would be to clamp a spacer under the mitre box to raise its top to 140mm above the table, hold the material tightly against the box, and cut part-way through the material. 

The cut can be finished off by placing the material inside the mitre box as usual.