Boil it down!
There's a trend I've notice within the poly community, also commonly seen within the mono world. The majority of drama seems to originate from people getting overly vested in relationships early on, feeling very hurt and upset when partner selection hasn't been optimal, then seeking outside validation for their feelings, and more key, their actions in response.
Put me first in line to admit that when things don't go my way, I get upset. When it involves another person I care about, my Momma Bear comes out, and I usually feel vested in protecting them, even from the fallout of their own choices. How useful is that? Not so much!
What I'm finding helpful at this point, is to look at things in the most essential components. Let's say I got into a dating connection with someone, then find out a few dates in that there is an essential piece of compatibility missing that is going to put this into the non-starter camp. Now, I could spend a bunch of time and energy being upset that this isn't going to go, because that is disappointing, almost in the same way that being rejected would be. However, when it comes down to the bottom line: I dated someone. In that exploratory process, it began to look like a no-go, so we have a conversation about that, thank each other for the time spent, and move forward with a minimum of hurt feelings.
Where I see this process go sour in most poly situations is that outside influences (read: other partners) are often seen as a contributing factor in the no-go. For me, this isn't any different really than any other base incompatibility. "Hey, I really like what you have to offer, but don't think I fit well within your existing structure.". Yes, I blaspheme! Why should existing partners have any impact on future partner choices? Because they do, or you like to live in a compartmentalized world where there is no contact between the moving parts in your life.
On to the next big challenge: People seem to expect that, just because they are interested in forming a relationship with someone, that it's reciprocated. This one has put me in hair-pulling mode more than once, on both sides of the equation. It completely sucks when someone is either just not that into you, or panting to do whatever it takes, if only they can be with you! It is uncomfortable and/or painful for everyone involved. What did the more-vested person do wrong? Nothing. Their feelings just clicked in too hard, too fast. What did the less-vested person do wrong? Nothing. They just didn't get on board the train. Yet, time and time again, it is seen as a blame issue that must be apportioned fault.
Try this on for size: "I'm sorry, but my feelings for you just aren't at that level.". Keep it simple, and remain compassionate. Stay aware that you aren't obligated to fall in love with someone, regardless of how much you respect them, enjoy their company, like having sex with them, or how passionately in love with you they have become.
When the swirling winds of emotion threaten to overwhelm the good sense I try to retain, I just boil the situation down to the simplest factors. Often, this creates a different level of clarity, perspective and understanding of the other views represented. It's well-worth the time and energy spent to detach from a desired outcome. Sometimes, a situation you viewed as extremely personal becomes much less scary or hurtful when you take the time to distill it to essential components. Remember, sometimes a sausage is just a sausage!