Se cortó el agua
Refers to the flow of water mains have been cut.
So it's like saying:
El flujo del agua se cortó.
It is the tilde(Accent) sets the third person of the singular, of the first prerson.
Yo corto pan. - I cut bread.
Pepita se cortó el pelo. - Pepita got a haircut.
"se" can be used if you use "usted" too.
Usted se cortó el dedo sólito.
"Usted" is an third person of singular, but it means "tú" a degree of respect, at least in the correct use of language, as in many countries "Usted" not charge any sense of respect.
How "Usted" it possible that this is the third person singular and second at the same time?
Because it is used as a second person instead of "tú", but it really is the third person, as "usted" means "vuestred" - "Vuestra merced" It is similar to the English word "your self" what does it mean "tú y tu persona" (Your body and mind, nonsense respect of the Middle Ages)...
Usted was used to speak with a degree of respect for people without titles like "su santidad", "su excelencia" "su magnificencia" was descortez mention the other person directly saying "tú, or "vos", it was disrespectful.