Probably you are talking about sooty mold. This is growing on the sugary secretions of the whiteflies and/or whatever other sucking pests are present. Focus on getting rid of the bugs. Control of whiteflies can be tough. Maybe search "organic whitefly control" or "whitefly control organic" etc.

A heavy infestation might cause some branch dieback or defoliotion (abnormal dropping of leaves), I suppose, if that is what "slowly killing" consists of in this instance. Otherwise, maybe there is actually a third problem present.

hi kasi 77,
have you found any solutions to your mock orange problem? We have the same problem, as per my posting some time ago, and I have not found any solutions. All the hedges in the neighborhood are dying back.
Thanks for any update you have.