Hello and welcome to the Flow forum! 
If they want to supersede your current queen, they will keep trying even if you remove the queen cells. 
It may be that they are unhappy with her for seem reason that they can detect, but humans can’t. Perhaps she isn’t well-mated, or she is aging or her pheromone production is dropping.
I would suggest requeening with a good queen from a reputable supplier. I don’t know where exactly you are, but there are africanized bees in central and southern Florida, and I wouldn’t let a queen mate naturally in those regions. If you are anywhere near Winter Haven, you could pick one up, otherwise you can order one for shipping from Mann Lake. I have ordered several queens from them over the years, and they are very nice quality: