Unique premise, intriguing protagonist. He's not a Gary Stu or a harem lead who shows off to girls, he's someone who is desperate to free himself from his timeloop so he can kill everyone, for unknown reasons. It is very violent, and he does constantly try to kill people, so if you need that in a series, this is fine.
High quality art, protagonist is a murderous psycho, but a likeable and complicated one. He's smart and determined but not infallible. Plot so far has been solid. A lot of people in the comments seemed to be worried cliches were getting flagged and it would fall into them, but it turned out groundless, so don't worry.
To address Mr/Ms. Completely Stupid's issue, he had absolutely no reason to not wait until the next day (he's not on a timer or anything), and in fact it was probably a good idea as an anomaly had popped up and he wanted to investigate it first before muddying the waters randomly by chasing down a now-scattered group of people for no reason.
His goal was to systematically go through the school to find the time user, not to murder arbitrary students. I don't know why you had the impression he was in a rush. He spent probably at least several weeks being a student before deciding to go after the entire school. Don't read this if you just want to see a 1-dimensional moron instantly flex on everyone who crosses him.
I don't normally give 10/10 ratings for series that aren't either long or complete, so this is around an 8 or a 9, but I'm giving it a 10 because its average is ridiculously low considering the quality and lots of people give 10s on much less interesting series.