Crumble sausage in a large skillet and cook over medium-high heat until no longer pink, about 5 minutes. Drain excess grease.
Turn on a multi-functional pressure cooker (such as Instant Pot®) and select Saute function. Add olive oil, onion, and jalapeno; cook for 3 minutes. Add chili powder and cumin and cook for 2 minutes more. Stir in sausage, beer, and tomatoes. Close and lock the lid. Select Manual; set timer for 5 minutes. Allow 10 to 15 minutes for pressure to build.
Release pressure using the natural-release method according to manufacturer's instructions, about 5 minutes. Carefully release remain pressure manually. Remove the lid. Add Cheddar and Monterey Jack cheeses; whisk vigorously until melted. Serve immediately.