Ameila, my husband grows melons and he never pulls them off...don't quote me but I think he said that the vines put down to absorb more water and nutrients from the soil. He has always had pick up loads of big watermelons. One year he filled the concrete floor of his wood shop which is really big to keep them until he could get rid of them. This year his patch is very poor due to the rains we have been getting.
The only time I cut watermelon or any vine, for that matter, is now, at the end of the season. And then I'm only cutting the new growth down to the next fruit on the vine. That way, the plant concentrates on the fruit already on the vines and not on the next blooms, too. But then I'm in a short-season area and this practice is necessary to get ripened fruit out of a plant that is really a long-season plant. I don't get very many fruits, but I get enough.
Farmgirl Sister #35
"If you can not do great things, do small things in a great way." Napoleon Hill (1883-1970)