If you’ve never done it before then no, it isn’t near big enough. If you have then sure, it’ll kill deer or even bigger stuff further than the stated range and with “worse” bullets as well. At least this is what you will generally glean from answers to this type question here on the fire.

There hasn’t been a deer born I’d be afraid to shoot with a 223 at 250 yards, I wouldn’t go out of my way to use a super hard bullet either. If you can shoot a 223 can be a pretty big gun.