Obviously, your partner needs to get over this. It's not uncommon for men to express fear or panic, as anger. That's probably what he's doing. But if he doesn't return to reason soon, you really need to give him a good talking-to. He has no justification for hating your mother.
She is who she is. She has the limitations she has. They weren't any secret to you or your partner, before the day the baby fell down the stairs. She's slow. She's not meticulous. She gets distracted by her own needs, like cigarettes and naps. You wouldn't expect your Polish grandmother to turn off her accent when she's watching the baby, because you're trying to teach him perfect English. You wouldn't leave him with a 7-year-old babysitter and tell the sitter to act like an adult while you're gone. It's just as unreasonable to imagine your mom's love for the baby can make her be someone other than she is, while she's watching him. You and your partner - the ones ultimately responsible for the baby - must decide: is it safe for her to keep being around the baby without supervision, now that he's more mobile? The answer's inconvenient, but probably kind of obvious.
If I sound unsympathetic, that's not what I intend at all! We're dealing with the same issues. Both my parents and my MIL are in town, and DH and I have a 3-year-old. All 3 of our parents were accustomed to watching our older kids, all the time. And, since the older kids are pre-teens and teens now (and more or less able to care for themselves for reasonable periods), our parents can still "watch" them (i.e., come over and visit with them and feel like they're helping DH and me). But my MIL cannot catch our toddler. So we've had to be very clear that if she watches him, they have to stay inside. Even if it hurts her feelings, that's the deal, or she can't stay alone with him. A serious accident on her watch would upset her much more and cause a much bigger rift in our relationships with her. Actually, she's really cool about it. She knows she has mobility issues. It's more difficult with my Dad, who's recovering from a stroke. He seem to think he's back, 100%. But there are times he just doesn't seem able to pay attention to details, or he gets confused about what he needs to do. He always offers to watch the baby for us. But we just have to say no. It would be great if we could take full advantage of all the willing, loving, free child care that surrounds us. But, again, we can't expect our parents to be different people, just because we need them to watch the baby.