Are there certain types of foams I should not be cutting?
Yes there are certainly foams you should exercise caution around when cutting. And an easy way to check what cautions you need to take when working with different foams is to look up the foam's specific MSDS report.

MSDS stands for Material Safety Data Sheet.

"A Material Safety Data Sheet (MSDS) is a document that contains information on the potential hazards (health, fire, reactivity and environmental) and how to work safely with the chemical product. It is an essential starting point for the development of a complete health and safety program."

Definition taken from the Canadian Centre For Occupational Health and Safety

https://www.ccohs.ca/oshanswers/legisl/

Here's a couple of examples for MSDS reports for different "foams". The first is the MSDS for rigid foam insulation the other is for Polystyrene Foam. The last link is for the rigid pink foam insulation.

Some foams are safe to cut (knife, saw or heated wire) the other foams require personal protective equipment (PPE) just to be around.

Learn the material you want to work with and study its MSDS sheet before doing anything with it.

https://www.kasteel.ca/wp-content/uploads/2015/07/MSDS-Polarfoam-PF-7300-0-Finished-Foam.pdf

http://www.styreneproducts.com/media/files/SPI%20EPS%20MSDS(1).pdf

http://insulation.owenscorning.com/assets/0/428/429/434/896b50d3-24ef-4263-997a-62927ac03237.pdf

I think there was another question here on the exchange which talks about the importance of MSDS sheets. If someone knows the link then please edit this answer to include that post.