I thought about that too but I think she might’ve just seen that his arm was gone and made an appropriate threat about it at the end like all good villains do.
I believe that if Ashe really did have something to do with it, McCree wouldn’t have been so willing to start with banter in the cinematic as he did. He seems rather passive about Ashe, if anything, like she’s not a big deal. Had she been the cause of his missing arm, we probably would’ve gotten a less, cartoon-y ‘old standoff’ kind of movie and more of a tension filled moment between two ex-lovers who became enemies or at the very least, two old friends who became enemies.
I’m not sure if we’ll ever really get a canon story about how McCree lost his arm. Someone on the Mcsombra discord came up with a really good headcanon on how Ashe might be linked to his missing arm – it’s really good, but again, I think the mood of the cinematic would’ve been much different. It’s obvious that Blizzard wants to portray McCree more as he is in the present, more light-hearted, probably not as aggressive or confrontational, which explains his more confident and laid back approach in the short.
Edit: I wanted to make a note that reasons why people MAY think Ashe might have something to do with his missing arm, is because, like OP states, her comment about having BOB rip out his other arm makes it sound like she ordered BOB to do it in the past. There is also the fact that Ashe doesn’t react to McCree like she hasn’t seen him in over 20 years…she acts like she’s seen him a few years back, possibly after he left Blackwatch but before the most recent events. She doesn’t seem shocked to see McCree is still alive, says ‘you promised you’d write’ and doesn’t seem to note McCree’s arm, like Echo did when she asked what happened. That can either mean, Ashe did have something to do with it or she saw him recently, just after the incident where he lost his arm.