My whipped cream can has run out of nitrous. I want what's inside anyway. What's the least destructive method of doing so?

Circular saw will fill it with metal filings - not great for the mouthfeel, I'd think.
Pliers aren't sharp enough to puncture.
Can opener will have no lip to grab.

Your first issue will be the container skidding out of your control - with potential for finger-loss & furniture damage. You're not going to easily find any implement you can squeeze slowly to make the first cut, you're going to have to hit it with something sharp.
Your second will be how much gas is actually left in the container & what that results in.

Messy but possible, grip it in a vice & puncture with a hammer & fine wood chisel. Then use something like aluminium sheet cutters (they're like big, tough scissors) to finish cutting around the perimeter.

Cons:-

1. Spray/spatter on your first puncture, assuming you can hit it hard enough to penetrate the top face without going straight through & pouring the rest on the floor.
2. Sanitising the tools.

I'd just bin it.

This may be the solution you’re looking for

1. Make sure the pressure has all been released
2. Lay canister on the counter with a towel underneath (or something to help keep it from sliding around). Or, place upside down in a stable container that won’t break or slide.
3. Use church key to puncture the bottom. (Additional leverage may be required)

I haven’t tried it but a tool for cutting metal tubes could work. Unlike a saw it doesn’t create particles and the cutting surface is pretty clean and smooth. They are commonly available up to 35mm diameter, not sure if this is sufficient for a whipped cream can.

Place in the fridge with something holding the top down. Leave for 15 minutes. As it cools, it will suck in air. Remove from fridge and wait until it warms up. A small quantity will be released. Repeat until all is purged.

Try grinding the bottom lid off with an 10" file. It will take about 10 minutes of filing and the lid will come off in one neat piece along with a ring of metal that remains from what used to be the lip. Or you could grind the bottom lid off by rubbing the can's bottom on the surface of a cement sidewalk like in the YouTube video "3 Awesome Ways To Open A Can Without A Can Opener"

Ensure your are alone because the following would not be considered good manners.

Just like some baby bottles, suck cream from can, can above mouth. Move valve to side to open. After some cream comes out, let some air go back into can. This will give you about 5 g of cream every cycle, which is enough to go with a bite of food that tastes good combined with cream.

Another option similar to Debbie M's answer, you could use a screwdriver and a hammer to poke a hole in the side, near the bottom.

Because your goals are not entirely clear, I'll assume that you are approaching this from an angle of waste reduction. Likely, you have run out of N2O on several occasions and you want to use it all up.

I think your best bet is to stop buying cans of whipped cream and start buying cartons of heavy whipping cream. It's cheaper, requires no N2O to whip up, and there is just a carton of waste when you are done instead of a can and whatever cream is trapped inside. Whipping up your own cream only requires a small amount of extra work, but you can sweeten and flavor it to your own taste!

The valve is plastic. You can puncture it by hammering a nail through there. A long enough nail will dislodge the internal straw, and allow cream to dribble out. The church key method looks good, if they still make the cans that way.