Dead roots on orchid

Judging by the photo, those roots might not be totally dead, so I would not cut them. As far as stimulating root growth, you basically have three choices:

1. A product containing rooting hormones, such as Dyna-Gro KLN or Superthrive.
   
2. A product that contains high levels of molybdenum and boron, which stimulates the plant to increase its own production of hormones. Mega Thrive is the only such product I am familiar with.
3. Kelpak, which is a very complex, natural but powerful biostimulant.

Kelpak is my recommendation, as it acts something like a "plant IV" in addition to being a root growth stimulant, giving the plant the added resources to grow and survive. Rooting hormones stimulate root growth, but the plant is stuck using the resources it has already has produced, which weakens it. The Mega Thrive product is very powerful, but like the hormone products, it requires the use of the stored plant resources, plus anything treated immediately becomes toxic to birds and mammals, so pets and small children (who put everything in their mouths) must be kept away from the plants.

Kelpak has been used worldwide for over 40 years on foods, fruits, nuts, grains, turn and shrubs; I "discovered" it a bit over a decade ago and brought it to the orchid world.

 

The leaves don't look dehydrated... yet
So the roots are still viable at the time. I would just incubate it in something makeshift (a germination tray and dome works great), giving it high humidity and light. Mist the roots 2-3 times a day.

 

And don't cut roots. A bad root can still hydrate the plant though not as efficiently as a good one. If you cut roots, there are NO roots, and no way for the plant to get hydrated. You can consider tidying it up after it grows a new root system, let it recover before trimming anything.