Cutting Homasote, I use a Bosch jig saw, fine metal blades and a Shop Vac with a HEPA filter holding the hose inlet right at the blade. When done carefully this can be done anywhere.
The other alternative is to use a Airways # 6 flooring knife available at flooring supply stores and HD.
Couple of passes with a sharp blade and you have a clean dustless edge.
Using either method, I the use the Shop Vac with a 5" disk sander and or trim router for final finish with the same clean results. However the vacuum hose has some bite marks in it from the router.
A strong vac with a clean filter can permit indoor cutting. Just make sure the hose is right at the point of dust source. When using a trim router I hover the hose inlet right over the pattern bit. Over the years the hose may be a inch or two shorter 
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