Using the past tense certainly implies that brother has died, but this is not universally true. For example, in narrative it's common to backshift all verbs to the past tense.
Not long ago there was a man with four daughters, and each of the daughters had a small dog. One day the daughters were out playing with their dogs when suddenly ...
The present vitality of the dogs is ambiguous, and in fact unimportant to the story. Because backshifting is a common narrative device, with your joke you should not assume the brother is dead. Another example:
When I was growing up I had a brother who used to get into all kinds of trouble.
From this, you could not definitively say that my brother is now dead. Again, in the context of the story it doesn't matter, and you'd have to explicitly ask if you wanted to know.
Anyway, the main point of the joke is to recognize each of the daughters would have the same male sibling, and not four separate male siblings -- but, with the given information, it's impossible to say whether this brother is alive or dead. You'd have to ask.
Related note: As if that wasn't confusing enough, it's also common to use the present tense to talk about historic figures now deceased, especially when referring to the current effects of their past work:
Even though he died when he was only 52 years old, William Shakespeare is still considered the most influential writer in all of English literature.