It's probably too late now. We seem to have lost that battle in the 14th century, when immigrant words were crowding in, boeuf among them. It was in Linda and Roger Flavell's delightful Dictionary of Word Origins that I found an explanation of how we came to use the French-derived beef, mutton and pork for the meat, and the English ox, sheep and pig for the same animals on the hoof: the English peasants had reared them, the conquering Normans had eaten them. This may not be entirely right, for beef (usually in the plural, beefs or beeves) was still a word for the animal, as well as for its flesh, only 100 years ago; but the principle is sound - French for the nobs, English for the workers. Then the fashion for putting menus in French confirmed today's usage. (The French returned a dubious compliment when, they called us rosbifs).
Beef's further meaning of muscle or effort, apparently first used in the 19th century, is clearly a reference to the live animal. So is beefy - though Horace Walpole, who may even have invented the word, used it differently when he complained to his friend John Chute that his neighbours ate so many roasts that they became "mountains of beef", and that he had an aunt, "a family piece of goods", who was as "beefy" as the rest of them.
The verb "to beef", which we got from the States, may originally have meant to behave like a tiresome steer which kicks up a fuss about going where it's told; the OED has a quote that suggests this, but it sounds rather contrived.