Definitely an interesting question. I will try to answer it using list of causes of death from Wikipedia (the table contains rather old data, but it has improved readability over the newer one provided here).
Short answer: No major changes are to expected in the top causes of death, except for the first two major causes: Cardiovascular diseases and Infectious and parasitic diseases.
Disclaimer: the following is not intended to be mathematically precise, but rather a qualitative analysis (lots of assumptions and rough approximations are used).
So, the main causes of death along with their frequency is the following (I am considering main groups only):
- Cardiovascular diseases: 29.34%
- Infectious and parasitic diseases: 23.04%
- Malignant neoplasms (cancers): 12.49%
- Respiratory diseases: 6.49%
- Unintentional injuries: 6.23%
According to this source:
[...] vegetarians had a 24% lower mortality from ischemic heart
disease than nonvegetarians, but no associations of a vegetarian
diet with other major causes of death were established.
This means that virtually, only cardiovascular diseases mortality (which contains ischemic heart disease) is greatly influenced by being a vegetarian or not. So, it is a chance that the 6% difference can be gained by the vegetarians. Also, the other causes of death changes changes are expected to be very small (except for malignant neoplasms which is detailed below).
According to this article:
[...] vegetarians are 45% less likely to develop cancer of the blood
than meat eaters and are 12% less likely to develop cancer overall
12% is clearly too low to make a position change in the top.
So, my opinion is that the most probably main causes of death for vegetarians should be the following:
- Cardiovascular diseases: ~23%
- Infectious and parasitic diseases: ~23%
- Malignant neoplasms (cancers): ~11%
- Respiratory diseases: >6.5%
- Unintentional injuries: >6.2%
NOTE: I have scaled mortality rates with the reduced change of dying from that particular disease (where sources indicate that mortality rate is significantly changed by being a vegetarian). I expect that it is not that simple, but close enough for our little top.
It is very hard to evaluate how non-cardiovascular and non-cancers rates are changes, but there are expected to be greater.
Other reduction used is that the ratio vegetarian/total population is very small (this table indicates it somewhere near 5%).