There may be several reasons for this behavior. The swan may be hot or stressed. Under these situations, the swan may actually look as they are panting.

If the swan has food or other substance impacting its nostrils, it may be breathing from its mouth because it cannot take air into through its nostrils.

If the swan has food, fishing tackle or something else located in its throat, it may be trying to breath as well as dislodge or mitigate the effects of a partial blockage to its airways.

If this is a cygnet or juvenile swan, there is a possibility that it has an infection or a possible genetic problem with the nasal passages.

We would suggest that you contact the local RSPCA or other wildlife agency/facility/rehabber to come out an capture the swan to check if something is wrong. If the partial blockage or whatever else is impeding the breathing becomes a total obstruction, the swan can die. The Regal Swan