Likely, but I don't think the other party has a high chance of winning said case. The problem is causation; your dog caused the incident, but its not a foreseeable harm that the other man would be injured by his own dog. Usually when a dog gets loose a reasonable person expects that the dog that escaped will do the injury, not the other animal.
You could also say that the other man contributed to his injuries as he was careless while separating them. Please seek a personal injury lawyer for legal advice.
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