In Star Trek (2009), the Narada is equipped with some sophisticated missiles. Why would a mining vessel need such heavy offensive weaponry?
This is mentioned in Star Trek: Countdown comic series which is prequel of Star Trek (2009) movie. This comic series is officially 100% canon.
After Romulus got destroyed, Nero became mad. He blamed Spock (and, Vulcan) as well as Ruling Council of Romulus (which didn't listen Spock's calculation about dangerous Nova). Council members escaped with senate shuttle, but not his wife (and upcoming offspring). So, he killed all of them and grabbed their encrypted senate codes.
When he broadcasted those codes at the location told by feared council members, a secret Romulan facility appeared and assisted them. The secret facility was full of mind - blowing innovations which included advanced Borg technology.
As a new administration, he ordered them to convert his mining ship into war machine. His plan was to take revenge from Vulcan (which delayed in sharing red matter research) and Spock (who didn't create red matter on time).
His mining ship was now very powerful. He destroyed entire fleet of Klingon. And, even smashed USS Enterprise (of that time) very badly. He was about to destroy it, but he had no time (he needed to deal with Spock).
Unfortunately, when he caught Spock near red matter singularity, he was trapped by black hole & appeared in 2009 movie.
So, at the time he was trapped by Black Hole, Narada was no longer a mining vessel. It was a war machine able to challenge entire worlds of his own time (24th century).
According to the comic books (non-cannonical, but released at about the same time as the film), the Narada was outfitted with borg inspired when Nero was at the Vault, a top secret Romulan facility.
All mining uses what can be considered weapons. The oldest mines used horn picks and wooden clubs. Later, metal picks, shovels, and rod & hammer sets took over. Then, explosives and drills were added. Grinders are just automated hammers in batches.
The industrial cutting tools of the Trek era are Lasers, Phasers, Force Fields, Anti-particle beams and antimatter bombs. A mining ship is a large cutting system. Therefore, it has lasers, phasers, force fields, antiparticle beams, and/or antimatter bombs. All of which make pretty good weapons...
The Narada having these is eminently logical. The quality of the fire control is of course going to be near military, as mining is precision work; it's probably shorter ranged than equivalent military, but what's current military tech of 1979 is likewise now usually obsolete civilian tech.
I agree with aramis. A mining robot needs to have very strong weapons to dig tunnels in hard rock, and needs to be armored to survive falling rocks. Stanislaw Lem has a story about hunting a damaged mining robot on the Moon (with captain Pirx as the protagonist) and it tells as much explicitly about why this robot has strong armor and laser weapons. What makes this one especially dangerous is that it's not an Asimovian robot and so doesn't have problem killing people after its brain gets confused from a severe physical injury.
Isaac Asimov also has a few stories about mining robots, including Robot AL-76 Goes Astray.