Mice can't climb stairs in same way that animals with longer legs can, but they do have a 1-foot vertical leap that allows them to make their way up stairs easily. This ability to jump helps mice escape from danger.
Due to their small stature and slow speed, house mice typically practice avoidance to escape or elude danger. Mice can only run at speeds of 7 to 8 miles per hour, which is much slower than the average predator. Mice can fit inside of small holes and cracks in walls that are only 1/4 inch in diameter. Because of this skil, the National Pest Control Association calls them the "Houdinis" of the animal world.
Mice have excellent hearing that allows them to detect approaching threats. This excellent hearing capability is augmented by the fact that they have escape routes planned in advance. For example, deer mice live in small areas that allow them to learn the surrounding terrain well. The mice set up routes in protected or hidden areas that allow them to hide easily and limit exposure as they move from place to place. Mice also use their coloring as camouflage to hide in plain sight, allowing them to escape notice in both country and city environments. When mice can't escape, they defend themselves by biting and scratching.