Hi Jen, welcome to TG.

I'm afraid I have no knowledge at all regarding CoCut software or Mutoh cutters.
However you seem to have done your homework and bought CoCut which (on reading about) appears to be a good choice for cuttng directly from CorelDraw.

As far as installation, there's not really much that can go wrong if you follow the manufacturers instructions.
Make sure the hardware drivers are installed first and Windows is communicating with it. Then install your CoCut software. Somewhere in the setup routine you are likely to be asked to select the plotter/cutter model you will be using and (hopefully) as you have this installed already, it should show up as an available option.

Setting up the cutter and knife is again a matter of following the manufacturers instructions and doing a few test cuts.

If you're a seasoned CorelDraw user, you should have no problems, if you are new to CorelDraw then this might represent the biggest learning curve.