The sports match test
Ver un partido = to watch a match (as a spectator). Mirar el marcador = to look at the scoreboard (a deliberate action). You watch (ver) the whole game; you look (mirar) at specific things during it.
¡Mira! as an exclamation
¡Mira! is used constantly in spoken Spanish as a filler or way to draw attention — similar to "look" in English: Mira, no es tan difícil (Look, it's not that hard). ¡Ver! is not used this way.
A ver
The phrase a ver is extremely common and means "let's see" or "let me see": A ver, ¿qué tenemos aquí? (Let's see, what do we have here?) It always uses ver.