Difference in usage between "beware of" and "mind"

Solution 1:

When you say "mind" you are saying "be aware of" or "be careful with" not to be confused with "beware of".

They might overlap, depending on why you may want to be aware of something. You might need to "mind the dog" because he bites or you might need to "mind the dog" because you are about to absent-mindedly step on it's tail.

"Beware of your head" is strange sounding. "Mind your head" means to be careful with your head. "Beware of" in this context implies that your head is going to do something bad to you, whereas "mind your head" is meant to say be careful not to let something bad happen to your head.

Solution 2:

If you’re French, Laure, it might help to compare some of those expressions with what I believe might be the French equivalents. Beware of the dog is English for Chien méchant or Prenez garde au chien. Mind the dog could mean the same, but it is more likely to be found in contexts where it means Gardez le chien. Beware of falling rocks might appear on English road signs where the French would be Attention! Chute de pierres.

Beware of your head would be very unusual. It would normally be seen, on a sign above a low doorway, for example, as as Mind your head. Mind the gap is heard on the London underground as passengers get on and off and it is also written on some platforms.