Preheat the oven to 375 degrees F (190 degrees C).
Spread crescent roll dough out into an 11x14-inch jelly roll pan; pinch perforations and seams together to make a crust.
Bake in the preheated oven until crust is lightly golden brown, about 10 minutes. Let cool completely, about 30 minutes.
Mix cream cheese, mayonnaise, and vegetable soup mix together in a bowl. Spread cream cheese mixture over the crust. Sprinkle pizza with radishes, bell peppers, broccoli, cauliflower, carrot, and celery, pressing vegetables into the cream cheese mixture.
Cut pizza into squares, cover with plastic wrap, and refrigerate 8 hours to overnight to blend flavors.