what does means "“beat the ‘betes.”?
Or as he put it, making diabetes maintenance a
routine is the best way to “beat the ‘betes.”

Question

what does means "“beat the ‘betes.”?
Or as he put it, making diabetes maintenance a 
routine is the best way to “beat the ‘betes.”

Answer

It is just a funny way of referring to dia-'betes'. 
People come up with these types of phrases as mottos so that people are more likely to remember them. It is common in ad campaigns and public service announcements.