You cannot kill T. Rexes when you are a human. The one exception is the smaller version of a Rex in The Cave mission. Other than that, all your guns and spears can do is distract the Rex to come after you instead of your comrades. In most missions you must have the Rex come after you so that your comrades can open a door or complete an objective of some sort. Do not waste all your ammunition on a Rex. A few rounds of fire should be enough to distract it.