As stated, The Punisher is a violent TV show. Even by the standards of this universe, which is the darkest take on 'superheroes' we've seen, this one is particularly filled with blood and guts, which isn't too surprising given the nature of the character and the fact the show is created by Steve Lightfoot, who previously worked on Hannibal.
However, while there may be some hand-wringing over this, the violence hardly ever feels like it's done just for the sake of it. Yes, it is difficult to watch at times and there are some scenes - most specifically with Rawlins (the eyes) and Russo (the glass) in the final couple of episodes - that'll really make you squirm. But there's always a purpose to it, and a message beneath about what this violence means to the characters and how much it does (or doesn't) achieve.
That helps contribute to a dark, grim tone for the show, which again is in keeping with the character. Frank Castle is a tortured soul, and the writers and directors make sure we get all of that moodiness and sense of doom throughout, but with just enough humour and heart to stop it from becoming too unrelenting.
Both the tone and the violence marry nicely with the overall action of the series. It's not at the level of Daredevil, but then the brutal efficiency of Castle means it doesn't have to be. There are some exciting shootouts, and sequences where the show gets a little more inventive and has Frank stalk his prey in the darkness.