Place frozen venison and water into a multi-functional pressure cooker (such as Instant Pot). Close and lock the lid. Select high pressure according to manufacturer's instructions; set timer for 20 minutes. Allow 5 minutes for pressure to build.
Release pressure carefully using the quick-release method according to manufacturer's instructions, for exactly 1 minute. Unlock and remove the lid.
Break up any large chunks of meat, drain in a colander, and return to the pot. Add crushed tomatoes, beef broth, potatoes, carrots, celery, onion, Worcestershire sauce, garlic, and Italian seasoning. Close and lock the lid and select high pressure again; set timer for 15 minutes. Allow 10 minutes for pressure to build.
Release pressure carefully using the quick-release method according to manufacturer's instructions, for exactly 5 minutes. Unlock and remove the lid.
Stir in frozen corn, peas, and green beans. Put the lid back on for 4 minutes until frozen vegetables have cooked.