It is a suffix, but the word it is being added to is not English.
Doctor is a borrowing from Latin (via French) doctor in Latin is an agent noun from the verb docere meaning "to teach". In Latin, "doctor" means "teacher" (compare indoctrinate). Another example is motor, from Latin for "mover". The other cases of "-or" are either borrowing of Latin words, or a spelling of -er that has been influenced by Latin.
Now a suffix is not always added to a *word", sometimes it is added to a "stem" For example "astronomer" has the -er suffix added to the stem "astronom-" (from which we also get astronomy).
Sometimes there are sound and spelling and meaning changes. From "solve" we get solution. But the "v" has become a "u", and the meaning has widened. (We can talk a solution of salt in water), and not everything that looks like a suffix is one. Consider "finger".
So you can't always remove a suffix and get a word.