If you are saying that Mach 3 says you are cutting at 0.0625 and you are infact cutting at 0.375 then you would appear to have an offset working - either a tool offset, or a machine offset.
You do not say whether you have fitted home switches - but I will assume you haven't. I do not know Cut2d but you must make sure that you do not put anything in the program that is a tool offset, or length.
Jog your axis to where you want to start your program - i.e.the X0 Y0 Z0 position of the program. This is usually, but not alwyas, the bottom left hand corner of the table, with the cutting tool resting on the workpiece. Check that this is correct for your program
Press the Machine Code button on Mach 3, the surround will light - "RefAllHome" and the Machine Co-ordinates will go to zero. Press the button again, and the surround will go out. The display is now showing Program Co-ordinates - these should be zero - if they are not, zero each one by pressing the zero button at the side of the DRO.
You now have Machine and Program co-ordinates all at zero - i.e. there are no offsets on your machine, and if you check Config/Fixtures the table should be clear. Check, while in there, the tool table - this should be clear as well.
If you jog your cutter clear of the work, and press cycle start, it should now cut at the correct depth. If it does not, Cut2d must be putting in some offsets. Stop the machine and check the offsets table and see if anything has altered.