As @csorrows said, the way to use a waveguide or other gas laser is to mount it securely to the frame of the mechanism and use mirrors to move the beam position around.
Like this-
You could also have the first beam segment be vertical.
Regardless, it is strongly advisable to enclose the path in metal for safety (it is far too easy to end up looking down the beam path).
As for the motions, the beam does not care (within reason) that the length of each beam path segment changes.
So for example you could have "motion1" be the Y motion of the gantry and "motion2" be the X motion of the gantry.
Mounting the mirrors is not actually that difficult a thing to do.
The focal distance from the the lens to the work piece however, is critical.
But no more so than the distances and tolerances for Z motions in FDM printing.
As for the mirrors and lens, you must use items appropriate for the laser's wavelength.
That is the reason I mentioned first surface mirrors (to prevent internal absorption and reflections) and CdSe lens material.
ZnSe and silicon (believe it or not) will work fine for lenses too, and mirrors are not all that expensive (like less than $20 each).
You could also run a fiber optic cable from the laser output port to the head.
Think of it as a "Laser Bowden" setup.
Obtaining a flexible fiber bundle compatible with 10600nm could be an expensive proposition though.
FleaBay has a used medical CO2 wavelength fiber for around $150.
If the laser tube is lightweight enough you could mount it directly to the carriage and run the motions a bit slower to compensate for its mass.
Flexible high voltage wires are not all that rare.
With a diode laser module you can mount it onto the carriage directly in place of an extruder of course.
Or you could use a "Laser Bowden" style fiber optic (much easier to obtain in the diode laser's power and wavelength).
The problem is that the wavelength of the diode laser will readily penetrate your cornea and focus on your retina.
You could be injured or permanently blinded more or less instantly by lasers of the power being dealt with here.
10600nm on the other hand (CO2 laser output) does not really pass through your cornea so it would only cause surface burns.
Not fun and still serious, but far more easily treated and easily shielded against.
I have worked with lasers in commercial machining centers and personal projects for over 30 years.
I cringe thinking about the proliferation of high power lasers in a "hobby" environment.
You can buy them because the personal protection laws in China and places like that are lax or non-existent.
That doesn't mean they are safe or advisable to have around, and particularly not so if you have children anywhere around them.
I would not have a diode laser machining setup in my home. Period.
I have had several CO2 waveguide lasers (both Synrad and Laakmann/Coherant) in my home though while building machines and even showed them to neighbors (with safety glasses of course) while running.
