Are you absolutely sure they are fighting and not trying to mate? At this time of the year, hormone levels are rampant. The male will try to get on top of the female and will hold her head above the water, although this does not look like what is actually occurring. It appears that he is holding her head under the water.

The only other reason that a swan will try to kill a mate or cygnet is that something is wrong, entanglement or something such as illness or injury. In these cases, the swan will try to put the mate out of its misery. So, check carefully to ensure that nothing is wrong with the female swan. The Regal Swan