Not sure if I can add anything to the conversation that hasn't been covered yet, so I won't try to say the same things over. Others have akrwady replied better than I could. I will point out a couple interesting things though, even things written explicitly in the rules that your GM might have forgotten about.
Shadowrun to me isn't brutal, but it is dangerous. However, real life is dangerous too. Any Joe Schmoe can tussle woth the wrong guy at a bus stop and get his head kicked in. But it's far more likely that he'll just get beat up, have to go to a hospital, and maybe end up with a broken tooth and some nasty bruises. The point is, there are varying levels of danger in Shadowrun, and not everything is instantly LETHAL.
Let's assume the team frags up a run and gets into a firefight with some security guys, or Knight Errant, or whatever else. Depending on the nature of the fight, the orders the guards have been given, etc, the runners very well might survive. Maybe they just get tazed/gassed and in police custody. That's still bad, but who knows, maybe they could then call in ALL their favour abd have another team bust them out once they get on the bus on their way to prison. In this case, they'd likely lose most or all of their gear, have criminal SINs, gain some hefty notoriety, etc, but they'd still be alive. And at the end of the day, that's often all a Runner has in the Plus column.
Or maybe they don't even go to jail. Say a Runner team gets caught on megacorp A's turf, but one of the team members has a contact with said corp that's connection and loyalty 5. He pulls some strings abd gets them released, but now they owe him a BIG favour, and rest assured he WILL collect. This is still bad stuff, but not instant death.
Now, let's assume the runners get into a real shit show of a fight, maybe against HTR guys, Red Samurai, Toxic Brony Cultists, whatever, abd they start taking enough damage to straight up kill them. Shadowrun has in 4E and now 5E this cool rule about burning edge to save a character from certain death (if the GM allows and the situation warrants). Edge goes down permenantly by 1, seriously Bad Stuff happens, but not death. Maybe they get an arm crushed in rubble, their cybered especially get wrecked, they lose essence from a spell, etc, but if there's a way they can survive the situation, they do so. Your GM seems to either be coming from a game where this wasn't allowed and so he's unfamiliar with it, or he just doesn't like it and so won't use it. If it's the former, that's somewhat understandable, but if it's the latter it strikes me as just taking an already dangerous system and dialing it up to deadly, which is unecessary.
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Now, onto roles unfilled on a team. The other people who already posted before me covered this pretty handily, in that a team gets hired to do a job they are the right fit for, and it's the GM's job to tune the game to his players. However, what about those jobs where it was supposed to be a simple milk run abd they encounter an undisclosed obstacle they can't get past. Maybe it's a password protected node they knew nothing about, or the site has spirits as well as guards, etc.
People before touched on hiring other specialists to cover gaps in the team, and I wanted to point out that sometimes you don't even need to hire hire a full team member to fill in, but just pay for a service. In the 4E book Unwired, it s tually has s table listing costs for hacker services based on the danger and complexity of a task. So that password protected node? Maybe the team makes a quick call to negotiate a hacker to Crack the node for them, and then that hacker is done with them. Sane thing for a magician to summon a spirit for the team, or hire a sniper to provide over watch, etc.
There's actually a fluff story in one of the 4E books where Slam-o does just that. He's on a hacking job and cones up against a node or ic or something he can't get past (can't remember the specifics). So he calls out to a cracking group he's a member of, and ends up grudgingly trading a copy of the new custom-program he just wrote in return for what he needed to get past that obstacle. So that type of exchange actually has a place not just in the rules, but in canon fiction of the universe.
Anyway, points to take away are that the system is dangerous but not INSTADEATH lethal, teams should do jobs they're the right team for, gaps in roles can be filled on a number of temporary basises (basis'? Basies? Weird word), and if anything the higher danger level will encourage players to play smart instead of just relying on rolling well. Sounds a lot like your GM may need to be reminded of this.