Place cherry tomatoes, celery, and red bell pepper into a blender. Pulse a few times to get mixture moving. Blend on high until mixture has liquefied, a few more seconds. Place strainer over a bowl and strain mixture to remove seeds and skins. Push mixture through strainer with a spatula to extract the liquid. Season with salt and pepper.
Sprinkle flake salt, black pepper, and chili pepper on a small plate. Rub rim of a glass with cut surface of a lime. Invert glass and dip rim into salt mixture.
Fill glass with ice and add Worcestershire sauce, hot sauce, and soy sauce. Pour in the vegetable juice and juice of 1/2 lime. Fill the glass 3/4 of the way with ice-cold beer. Stir. Top off with more beer. Garnish with lime slice.