Stealing from James McLellan's answer, the flow rate of Jovian atmosphere through a 200 meter portal won't cause any large scale extinctions anytime soon. Even if the answer is off by a couple of orders of magnitude, the Lovecraftian horrors are going to need to gobble up Earthly life at a prodigious rate if you want your heroes to see a mass extinction before they die of old age.
On the other tentacle, the job contract for getting that portal closed doesn't specify doing it just in time to save 25% of Earth's species. Instead, the job is to figure out how to close it and execute the plan as quickly as possible. Maybe this requires a nuke. Maybe it requires some hideous blood sacrifice. Maybe it requires the "Open monster spewing portal from Jupiter" passage in the Necronomicon to be read backwards.
There's a small complication. Once the heroes have an idea of how to do it, they don't get to spend a lot of time practicing. Any instructions, be they from ancient scripts or from the Miskatonic University's specialist in trans-dimensional physics, aren't going to be as clear cut and foolproof as the instructions on a can of condensed soup.
So, while the world is focused on dealing with the monsters, our brave heroes slip in to close the portal. They launch the missile, press the activator on the dimensional scrambler, use sacred blades to carve the hearts out of 1000 armadillos, read the opening instructions backwards, or whatever. Then what happens?
A. Portal goes poof. Heroes get a parade. Roll credits.
B. Nothing. It was a great idea in theory, but it didn't work. Time to try a different method.
C. The portal closes. High fives and hugs begin, but then the portal reopens. Due to some tiny error in the closing method, the reopening portal doesn't stop at 200 meters or even 2 kilometers. Instead, it slowly widens to 200 km.
The end result of option C? The much larger portal unleashes far more creatures and seriously alters the composition of Earth's atmosphere. Even more interesting, the lower half extends downward past the crust into Earth's mantle, and that rock is hot, under extreme pressure, and not solid. A significant amount of mantle material will be sprayed into Jupiter's atmosphere, likely causing significant geological instability on the Earth side of the portal (and seriously annoying the leaders of the Lovecraftian horrors). Conveniently, the new version of the portal isn't stable, so the author can have it collapse at the desired level of destruction.
Congratulations heroes! You've sort of saved the Earth.
Edit: I jst thought of one ugly little detail. If that 200 km wormhole is over land, things mostly go as explained above. But what if most/all of it is out over the ocean. Then the lower half won't just bu nibbling crust above the magma spraying into Jupiter's atmosphere. The expected 20 or so atmospheres of pressure on the Jupiter side will push the water back until a bit short of 200 meters depth (might be off a bit here, working from memory and doing the math by counting on my toes). Below the pressure balance point is an area about 200 km wide extending to the ocean floor. That's now a river draining the Earth's oceans. A day or two should undo that pesky sea level rise problem, but if it stays open too long, you can add "major sea level drop" to the list of problems pushing species into extinction.
Ocean, land, or some of each, the forecast also calls for interesting volcanic activity. 😃