Combine sweet potatoes, coconut milk, vegetable broth, garlic, salt, and pepper in 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 8 minutes. Allow 10 to 15 minutes for pressure to build.
Release pressure carefully using the quick-release method according to manufacturer’s instructions, about 5 minutes. Unlock and remove the lid. Carefully remove pot insert and place on a trivet.
Mash sweet potatoes with butter in the pot insert using a potato masher and season with salt and pepper to taste.