For the purposes of this thought experiment, let’s assume we just need to take down Mr. Stay Puft and not the entire supernatural portal. (Because honestly, if a supernatural portal really opens, we’re just fucked.) Flamethrowers, which seem like the most obvious real-world weapons with which to melt a marshmallow, are no longer in the US military’s arsenal. In 1978, the Department of Defense stopped using the flamethrower in part because it was too unstable. A taser on the other hand might melt a small patch of Marshmallow Man if you get right next to one of its massive, fluffy legs, but as the destructor (presumably) doesn’t have nerves or muscles, a taser wouldn’t paralyze it.
If the city did evacuate the Upper West Side and surrounding neighborhoods—or hell, the whole island—then more powerful bombs could come into play. The Air Force’s McGuire-Dix-Lakeshurst is a short 75 miles away, and as Marshmallow Man doesn’t look especially nimble I’d imagine dropping a few bombs on him shouldn’t be very hard. The buildings of New York, however, might take a beating, presumably after an evacuation.
How NYC Would Respond to an Actual Stay Puft Marshmallow Man Attack (via Gizmodo)