If you are not aware of the plots then the deaths would usually appear accidental. Hunting accidents and the like. Or natural if the killer used poison. Or as @Phillip says "Under mysterious circumstances" if there is a suspicion of wrong doing but no proof. Which one you get depends on the type of plot and then very much on your intrigue value and that of the plotters to decide whether you remain blissfully unaware, suspicious or know it's actually murder. If you do know who the murderer is then the dead character will have a red skull by their picture and clicking on this red skull will take you to their killer.
It sounds like you most likely have a courtier whose current ambition is to become spymaster and is proceeding to kill their way in to the position. They will keep on killing as long as they are your courtier and are not the current spymaster. Go through your courtiers and see if you can identify who has the ambition and either appoint them or eliminate them.
If you can't find anyone then your previous spymasters must have had a relativley low intrigue value to be killed off so easily? It sounds like you need to get a better spymaster and place them in your capital to uncover plots.
The best way to do this is look for a lowly courtier in another country with a very good intrigue rating and invite him to your court, bribes will get them interested in moving but don't waste your money if they already have a high opinion of their current liege as the likelihood is they wont even consider it. Or you could look for young princess who are third or fourth in line and therefore willing to move as they want you to press their claim.