Hi
I have heard it said " cat's bring them home as presents"
If you scold him, he will think he's not got, a good enough gift & will go & get a bigger, better one.
You have to praise him & he should stop.
P.S, I haven't tried this, our cat eats & then welds itself to the duvet for 12 hours.
Tis true! Mind you I dont know if it would work with an adult cat - but we got ours variously between 6 wks and a year (all rescues) and they soon got to know what we approve of and what we dont.
Bird kills were ignored (as far as possible, humane-ness and chaos allowing) with bodies remove swiftly and with no fuss. Mouse catching and eating is actively admired and approved, consistently and however gruesome the process. The result is that birds aren't caught (unless they annoy over a period of weeks and then you have to understand if not appreciate) but when mice are caught, they shout for us to come and appreciate and approve before settling in to eat.
It took a while for them to figure out that voles and shrews didn't get approval - and they didn't like them to eat, so what was the point?
Eeeking and shreking wont help - cat will either take it as approval or as an inadequate offering. Either way, he'll do it again.
Note: when I feel sorry for a mouse - I remember that they are helping to save the dolphin. Mice breed fast and the population isnt damaged, but catching the tuna for the cat food also catches dolphins and they breed slowly and are at risk as a species. So, encourage them to eat mice and save the dolphin!