It's hard to tell from that photo. Maybe use some rubber cement on it to seal the ripped chunk in before you try to mount it again. You'll know soon enough once it's on, if it's going to hold air.
I suspect you didn't have the tire bead fully into the "drop center" section of the rim everywhere except where your were working. If it's not, a tire can become almost impossible to get over the rim without damaging it.
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