I don't have blue agaves but have other varieties. None have flowered yet but they are native here and I see flowers regularly in the wild. There seems to be a general consensus that cutting off the bloom stalk will not save the agave. The changes that trigger blooming also lead to death of the plant. The flowers are usually spectacular too, so you're depriving yourself of a treat - plus you can eat the flowers. I haven't seen any mention of edible agave fruit.
If you've taken good care of your agave it should be surrounded by baby agave that have grown up from the roots of the mother plant. Just dig these up and plant them wherever you want a new agave. They grow very quickly in rich soil with regular watering. The baby americanas and angustifolias I weaned off their mum 2 years ago are now about 40 cm across and producing babies of their own.
You can cut off the needle-sharp dried leaf tips to avoid getting speared by them. The leaves do quite well without them.
You can eat much of the agave too (http://www.gourmetsleuth.com/articles/detail/agave).
Thanks BajaJohn. Here is the reference I found.
"The quiotes start to appear in years five and six, and grow rapidly. A quiote can grow a meter a week, and if not cut down, after the third week they will start to extend lateral arms which will fill with flowers. Farmers send field hands through the agaves to cut down quiotes every two weeks or less, to be sure they don't grow too large and take away some of the plant's nutrients and sugars.
Cutting the quiote encourages the cabeza, or head, to fatten and grow richer with sugars. It also encourages the production of shoots. It will usually be harvested for tequila from six to 12 months after the quiote is cut."
" The piņa is ripe when it starts to shrink and develops a maroon tinge, and red spots appear on the leaves."
"Another indicator of ripeness is when shoots start to appear on the remnant of the quiote stalk."
http://www.blueagaveforum.com/tequila/harvesting.htm