Diabetes, together with its serious complications,
ranks as the nation's third leading cause of death, surpassed only by heart disease and cancer
It is basic question of Verb tense error check list.(a) ranks as the nation's third leading cause of death, surpassed only-> Diabetes is singular, like economics.

. So, ranks is okay and Surpassed only...two diseases is also okay. Let's keep it.
(b) rank as the nation's third leading cause of death, only surpassed-> Diabetes is singular, so "rank" is incorrect.
(c) has the rank of the nation's third leading cause of death, only surpassed-> Okay. We have verb tense error corrected. But, we have another issue. When we are comparing Diabetes, then we need to take other diseases in account. "Only surpassed" is incorrect.
(d) are the nation's third leading causes of death, surpassed only-> Diabetes is singular, so "are" is incorrect.
(e) have been ranked as the nation's third leading causes of death, only surpassed-> Diabetes is singular, so "have" is incorrect.
So, I think A.