hmm that is weird... so the laser is definately making it as far as the last mirror.
Have you tried doing a test laser at all four corners of the machine table? Ie go to top left, test laser, top right test laser, bottom right, bottom left?
That would be certain the laser mirrors are properly calibrated.
One thing i do notice tho (unrelated to your probelm) but the cuts seem very wide (maybe its just the charring), is it correctly focussed? The laser should have a preset focal point which would be a predtermiend distance from the lens head. If it doesnt have an autofocus youd need a measuring jig to set the table height. Ie if you engrave is the width of the engrave "fat"?