Yes, in most states the other person's property damage liability coverage should cover the damages the at-fault party caused to your car. Thus the side mirror and any other damage done to your vehicle should be repaired by the at-fault individual's insurance carrier which would mean that you would not have a deductible to pay.

If for some reason the other party's insurance provider denied the claim and you had to put the damage through your own insurance policy's physical damage policy, in this case collision coverage, then your deductible would apply.