There are multiple peer reviewed studies that point the link between meat-eating and heart disease, as well as meat consumption causing people to die earlier.
This was an experiment that followed up 44,561 UK men and women for around 11 years, and concluded:
Consuming a vegetarian diet was associated with lower IHD [ischemic heart disease] risk, a finding that is probably mediated by differences in non-HDL cholesterol, and systolic blood pressure.
This review looked at nut consumption:
nut consumption seems to protect against ischemic heart disease (IHD). Frequency and quantity of nut consumption have been documented to be higher in vegetarian than in nonvegetarian populations. [...] Importantly, nuts have similar associations in both vegetarians and nonvegetarians.
The thing about unrefined (raw) plant foods and cancer is rates for some types of cancer are lowered by eating your veggies, while other types of cancer don't seem as influenced by diet.
But overall, yes.
Our results suggest that vegetarians have a significantly lower ischemic heart disease mortality (29%) and overall cancer
incidence (18%) than nonvegetarians.
Note however, they also say:
In conclusion, the overall cancer incidence and mortality from ischemic heart disease were significantly lower, but there were no associations of a vegetarian diet with
all-cause mortality and mortality from circulatory and
This looks at some studies, and discusses the strength of the evidence and the criticism of it - particularly warning of confounding factors.
The study, published in the European journal BMC Medicine, comes on the heels of a 2012 Harvard University study that found people who ate just 1.5 ounces of red meat daily were more likely to die early deaths than people who ate less than that. The latest study, which chronicled more than 500,000 people from 10 European countries, found those who ate the most processed meats (including ham, bacon, sausages, and ready-to-eat packaged meats) were most likely to die prematurely.
The Vegan Health: Disease Rates page cites many meta-analyses looking at both mortality rates and heart disease rates of vegetarians compared to omnivores.