FAT causes diabetes (and high blood pressure and heart disease) NOT Sugar. Dietary fat clogs up your bloodstream preventing insulin from effectively doing it's job.
http://www.amazon.com/Neal-Barnards-Program-Reversing-Diabet...
Here's the Amazon link for book about the program and you can also read the reviews of many people who have successfully changed their for the better as well: http://www.amazon.com/Neal-Barnards-Program-Reversing-Diabet...
But the links between diabetes and animal products are pretty well established:
https://nutritionfacts.org/video/why-is-meat-a-risk-factor-f...
https://nutritionfacts.org/video/diabetes-as-a-disease-of-fa...
You might want to have a look at this book too:
https://www.amazon.com/Neal-Barnards-Program-Reversing-Diabe...