Why is the leftover water of an animal referred to technically as Sū'r (with a hamzah) instead of Sūr?

Because Sūr means a stagnant well, while Sū'r means running river water.
Because Sūr (without hamzah) refers to a city's boundary wall, whereas Sū'r (with hamzah) means leftover water.
They are identical in spelling and have the same meaning.
Because Sū'r refers to larger animals and Sūr to smaller ones.