When you inflate the tire to the pressure you ride at. If the cut pooches out like a grandma wanting a smooch from her grandkid, then sure, you probably ought to replace it. Especially if the tube can be seen bulging out as well. Assuming you are tubed.

Otherwise, it it rolls then ride it till it wears out or gives you repeated trouble from that same cut.

You got a flat when that tire was in good condition. Whose to say you won't get a flat with another new tire?