There are a multitude of ways you can play dungeon-bashing games in GURPS, with or without DF. One is basically DF style - high-powered heroes with cinematic levels of skill carving through hordes of monsters. You see this in DF Jade Regent and in my Felltower game.
Another is the same style, but with somewhat lower powered heroes - using templates from Dungeon Fantasy 15: Henchmen, for example. The henchmen are dual-use by design. You can go for DF On The Cheap. You can simply use Basic Set and make up 100 or 150 point heroes, without any regard to a specific template.
Even with those, though, you're less powerful but there are some "heroic" elements that make you stronger than you might be in a more gritty, down-to-earth game.
Having run DF for a while, and having run a lot of GURPS fantasy games before that, I think there are some things I think you need to do to make for a more "gritty" feel.
No Weapon Master Advantage - At the very least, restrict Weapon Master to a later add-on that's not simple to get. Weapon Master is basically a have/have-not situation in combat in DF. Having it gives a per-die damage bonus (nice!), but more importantly gives you half penalties on Rapid Strike and on Parries (and Blocks, if you wisely included shield in your WM coverage). This makes a big difference, because it changes you from, say, -6/-6 for each of two attacks and additional parries at a -4 (-2 with the right weapon) to -3/-3 and -2 (-1 with the right weapon). You're much better able to leverage your skill offensively and especially defensively. Spending the same amount of points on ST and skill (to get the extra damage and absorb the Rapid Strike/multiple Parry penalties) won't really get you as much, and won't help as the penalties add up. This is not even counting access to other cinematic skills, if you're using them.
There is a reason every PC fighter in my games has WM - even the martial artist who also has Trained By A Master (which works the same, more or less, but without a damage bonus). It's have vs. have-not, and the have-nots (the NPC and PC barbarians in my game) have less options in combat and need more raw skill to approach the versatility of those that do.
(Not that this is a bad thing, per se, but it's a flavor-changer.)
Removing access to Weapon Master, especially at the start, coupled with lower point totals to make high skills less common, makes for more danger from smaller groups of monsters.
No Heroic Archer - For the same reasons as Weapon Master, you'll want to restrict this. Archers with it can demolish archers without it. You aren't merely a better archer but a quantitatively different archer. It's the advantage for movie Robin Hood and Legolas, shooting arrows like machine-gun bullets and hitting everything. Get rid of this, and you don't end up with a single bow-armed Scout facing down packs of bow-armed orcs with calm poise and killing them as fast as the player can roll dice.
A different way to allow for better archers is to give them access to better bows, and be really harsh about what people are allowed to defend against at range (see Dodge This!). Allowing Zen Archery for long-shooting sniper types without the need for the short-range arrow-matic of Heroic Archer is another way to let archers shine without making them, basically, melee fighters with a lot of reach.
Trained By A Master is Okay - Oddly, perhaps, I suggest leaving access to TBAM. It's not cheap (30 points), and while it does give great access to cinematic skills and abilities, it doesn't give a damage bonus. This makes it more useful for "trick" fighters like martial artists, swashbuckler-types, and ninja-types than for powerhouse front-line fighters. It is still a bit of a have vs. have-not, but you can control this by restricting access to it. If you can only have TBAM with an appropriate Vow, say, or need for regular (time-consuming and/or expensive) practice, or it's limited to some odd class of training, you can ensure it's not a must-have for all fighters.
If that's still to cinematic, then cut down its cost and restrict it to unarmed combat, making it basically a Shaolin Monk-only kind of thing. Especially at lower point levels, this will mean an interesting but not dominant fighter. Their cinematic skills take some time and effort to be good at, anyway, so it's not often Blind Fighting or Power Blow is turn-to-turn dominant in the the way that multiple weapon attacks can be.
Extra Attack - Keep a close eye on this, since it allows PCs to compress a lot of effects (grab-and-throw, feint-and-attack) into one turn.
Cap starting skills - Finally, it's worth considering a cap on how good someone can be to start at any given skill. Even DX+5 or IQ+5 (for spells) can put a cap on the crazy heroics you get with DF, where a starting PC can easily top skill 20 in their main weapon while backing it up with a pile of advantages to make it worth better. A relative cap (DX+5, as above) encourages better base stats, while a flat cap (Nothing above skill 18, say) has an more absolute leveling effect.
Again, this is just a way to make for less cinematically heroic PCs coming out of the gate. It's not the only way to do so, and it's still heavily tied to how many points you give out. 250 point guys without WM will still be scary. 100 point guys will still be kind of weak with access to WM. But the things above will go a ways towards keeping a lid on the starting power of the PCs, and give you more of a old-school Man-to-Man feel to combat instead of a high-powered Dungeon Fantasy one. I personally love the high power level of DF, but sometimes I think nostalgically of the lower-starting-power games I used to run (often with the same exact monsters I use these days). The advice above is culled from running such games; it might not work for everyone but those are the big things I see that change the effective threat level of the PCs in combat.