|This depends on how much there is. If its seedlings, you can mow it, use a bag and be careful not to get the cuttings anywhere on your person when emptying the bag. There is the risk of the oils staying within the bag and on your mower for a long period of time. There is also the risk of walking through it and getting it on your skin. Even if you take precautions with covering your person, you may have it on the soles of your shoes. You just have to think it out before you decide to mow it.
Don't use a mulching mower either, you will just spread the cut up ivy and risk having the oils spread all over. You could get a landscaper to mow it but you still have the risk of them chopping up the leaves and stems and spreading it around. That would make the area unsafe to walk through.