Mathematically I am wonder would two binary wormholes radiate intense energy as gravitational wave as they get closer and closer together, I like to know what happens to the mass (or negative mass) for these wormholes?
Most wormhole solutions involve significant curvature*, so if they change rapidly over time we should expect them to radiate gravitational waves. However, exactly what happens is going to be tremendously model-dependent.
(Footnote: One can make wormhole solutions that lack curvature simply by topologically gluing together parts of the spacetime manifold. But it is less clear what it would mean to have the holes orbit each other in this case. )