Q: using my mac air as extra screen while cutting

YYou can't.  You can connect the other computer as a hard drive but not as a monitor.

IF you have an iPad, there is software that will allow you to use its screen with your Mac.

AFAIK the only mac computers that can work this way are the iMacs.

You speak of "mobile office", but also speak of a Mac Pro. It seems to me that you are mixing ideas here.

Here is what I think would make more sense: a second (large) display in your fixed office, and a laptop for your mobile office.

In a mobile environment, I would just forget about the second display. An iPad would not be that much extra screen space anyway, and you would be complicating your mobile workflow; it would require extra software on the iPad, which would likely introduce a lag. Just sayin'.