As you are selling (or exchanging) the property that have mortgage - you would need either to obtain the mortgage for new property or pay off the mortgage for the old property.
The equity on the old property will be rolled into the new property and will be used to calculate amount you need for financing.
1031 exchange that another party used should not make any difference to you. However because it is more complex transaction you have higher risk that it might be longer or might not be completed at all.