"Old grind" is usually used in the expression "the same old grind" -- which means, the same (maybe boring) work that you do every day to earn a living. Example: A. How has work been lately? B. It's the same old grind.
I think the idea is that work can grind you down, like coffee grains or sausage meat. In America, the phrase is often used humorously and to really complain.