As I said in another post there are nanosurgeons, and reviving people after death is a lot easier, within a certain time limit, in Cyberpunk. Unfortunately a lot of that requires bioware and other medical technology which is basically unmentioned in 2077. It does exist but it's ignored and not very defined. The relic's nanites could be considered a form of bioware. The Animals use bioware for gene editing, and Biotechnica has an advertisement in game for the same thing. A cryotank could have preserved both Jackie's and Saburo's bodies until they were repaired and then they could have been revived.Vic gave V a MaxDoc at the beginning of Act I, which, according to him, is a stimulant. Stimulants can increase heart rate. But if it so happens that that one doesn't, it still wouldn't help Jackie from bleeding out.
Therefore, we can conclude that there was no way of saving Jackie.