So, I've never actually run M&M 3E, but I was a player in a game for well over a year. So I can tell you (from a player's perspective) what my GM did to make combat less of a pushover.
1. The GM can give players a Hero Point in exchange for a supervillain getting another chance at success. My GM would do this all the time. If a villain failed a defensive roll, we'd get a Hero Point in exchange for them taking another crack at it. This helps supervillains last more than a round or two. (In D&D terms, it's a bit like giving Inspiration in exchange for a use of Legendary Resistance. And I highly, highly recommend this.)
2. Mooks will rarely be much of a threat. We never felt threatened by minions. (Think Superman going up against bank robbers, he's not going to break a sweat.) The minion type enemies are basically there for a bit of fun padding, rather than a challenge. Takedown gives someone the opportunity to wipe out minion after minion, which is the whole point of those abilities. Edit: Just wanted to add, we'd often go up against a supervillain team with added minions, rather than just a solo villain and some henchmen. That definitely made the fights feel more challenging.
3. Combat should never be the only thing going on during an action scene. Whenever possible, you always want innocent people in danger. Describe minions blowing up a building, and chunks are falling into the crowd. A fire breaks out, threatening people trapped on the top floor. Bank guards get hit with a freeze ray, and unless they get medical care soon, they'll be in trouble, etc. Even a scene with no innocent people around should have optional goals: perhaps there's a death ray slowly powering up. Unless the heroes can take it out, Cincinnati is doomed! This gives all those minions a turn or two of getting free pot shots on the superheroes who, yeah, could take them out easily, but doing so would mean failing the basic goal of being a superhero, which is being a hero. And speaking of hero, the GM should hand out Hero Points to people who pause Clobbering Time long enough to save the taxi driver before his taxi falls off the bridge, etc.
Finally, M&M 3E is an exceptionally easy game to break. While it's technically a game with a lot of rules crunch (complete with Build Your Own Powers), in some ways it's more like a narrative game where everyone has to be on the same page to ensure things run smoothly. Because with a dash of system mastery, a player character can become truly unstoppable. There's an old Reddit post about a PL10 character (the recommended beginning level) who is basically more powerful than the most powerful superhero in all of fiction. Seriously, without cheating you can basically make The Beyonder. That's just the kind of game it is. So if none of these tips help, I suggest picking up a copy of the Basic Hero's Handbook, and having the player follow those pre-generated archetypes, which are all but guaranteed not to break the game. They have some good ones, the Paragon is like Super Man but won't break the game, there's a Batman, a Human Torch, it basically hits all the favorites.
Hope this helps!