I relate to the mental anguish and powerful physical symptoms associated with situations like these. I've had times when I started to shake (teeth chattering and all) much like Violaine described out of anger and distress. I'm used to strong physical symptoms when I'm really distressed, unfortunately - I tend to suffer from nausea and fatigue and backaches but yeah, if confronted with a really agitating situation I have found myself shaking or feeling something which I assume is like road rage (almost like I could hit someone.)
I have mixed feelings about cutting people out. I can think of maybe three times I've tried to doorslam someone. They all got back in, but all the situations are different. One of them got back in when he came back and apologised years later (albeit somewhat indirectly, but then we were able to talk about it.) He had hurt my feelings badly and I had dreams about him for years. I thought he didn't care but some stuff got back to me through the friend grapevine to indicate that he did much more than I'd thought. So we re-entered each other's lives but things had moved on and changed so much that we weren't going to be more than acquaintances. At least amicable ones, which is good. It wouldn't be more now than a once a year Facebook message or something.
Another was a female friend I doorslammed, explaining to her in detail why I was doing it...! We were both reacting to things badly at that time. I should have told her how I'd been feeling about where our friendship was going before doing something that extreme. She kind of slowly clawed her way back in and ultimately we discussed it and things are ok again. I just need to be careful about communication pitfalls with her but otherwise things are fine.
Another was a guy friend who'd hurt my feelings badly on several occasions and just generally shown a lot of mixed messages, lack of care and general tendency to be a user. When I tried to doorslam him he came back and apologised (actually, that happened more than once with him...) and I was so touched that I wrote it all off. However, a few months later it fell apart (sort of) when I realised he was using me for free therapy and called him on it. There was no doorslamming - in fact, I probably tried a little too hard to leave the door ajar. If anything he came closer to doorslamming me, though it was more like a mutual decision to just let things drift apart. He did ask me to his leaving party before he left the country and I went to be amicable, but I don't think there's much trust or desire to maintain things left between us.
I didn't doorslam my ex boyfriend, as it just wasn't practical at the time because we saw too much of each other for unavoidable reasons. But now that we live in different countries the door has just kind of quietly closed. When he tried to friend me on FB a couple of years ago I didn't respond. He's not quite dead to me, but fairly close. I have no interest in ever having him in my life again and don't feel much over it. I think by the time I got through all the pain over that there was just absolutely nothing left except maybe a very faint resentment. There are a few other people, mainly in that same city/country, who I feel similarly about though they're not exes or ex-best friends. I just realised in retrospect that there was some crappy behaviour and disrespect from them, I feel no liking or respect for them and wouldn't want them around at all. Although, saying hello politely wouldn't be a problem, and if forced I'd do that with the ex too but hopefully as briefly as possible.
I'm in another "mutually drifting apart" situation now and would prefer to keep the door closed on the person, though it wasn't a slam. I don't think maintaining them in my life would cause me anything better than pain and discomfort. I'm still having dreams about them and a certain amount of distress and preoccupation with the situation. It's hard when it feels like there's uncertainty and unfinished business, which there tends to be. I would really love to wipe my memory sometimes, especially because when someone is on my mind, everything - but everything - reminds me of them, especially anything we enjoyed together, experienced together, discussed or joked about, etc.
Some people are toxic and you have to let them go or even slam the door. Some people it's not so much toxicity, but the emotional impact of keeping them around is not worth it. If they have behaved hideously you have every excuse to shut them out, but if it's more ambiguous (disappointed expectations, lower-level but ongoing hurtful behaviour, etc) it can be even harder in some ways. I'm wary about letting people back in though I guess a couple of times it has more or less worked out. I'm just at the point where I feel like if I have a gut feeling I shouldn't let them back in - even if they are not "bad people" - I just shouldn't. They will hurt me again, due to their insecurity and carelessness, and/or residual hurt feelings on my part.
Also, to get over someone (especially romantically) it's almost like I HAVE to dislike and resent them. I know that's not good, but I can't keep hanging onto the good stuff, it makes it harder. So there tends to be a long period of resentment and hurt and then - just nothing, which is blessed relief. But it obviously kills any friendship/relationship. If it's someone I was in love with or had strong feelings for I sort of go from the extreme of idealizing them and caring almost too much, to seeing everything they did wrong and dwelling on all the ways they hurt me. The Mr Darcy line in Pride and Prejudice applies quite well to me - "My good opinion once lost is lost forever."
I also kind of force myself to conclude that they don't care at all. The weird thing is, the evidence very much suggests that people want to keep me in their lives, with rare exceptions. They usually "want me back" in some form, eventually. It has surprised me with a couple of people because I myself said some pretty harsh and hurtful things to them when I reached that point. It seems there is something they miss but I get to a point where I think "that's their tough luck". Almost with a bit of vindictive pleasure, but I know it's to mask my own feelings of hurt.
In any case there is a huge amount of emotional fallout for me. It generally takes years before I can think of the person or anything related to them without at least some pain.
I question my own behaviour and my own motives so much when I reach this point. I wonder if I am disloyal and should have approached things differently, etc. The facts ultimately convince me otherwise because I have maintained many friendships for many years and am widely viewed as loyal. In fact, I know that sometimes I have put up with too much. But every situation like this that arises, even if there aren't many, I question myself agonizingly over what I and they could have done differently.