@cindisc
You can cut to your heart's content. All those long, gangly ones can be cut back to the soil-line if you wish, trim the brown stems off, leaving only a couple of inches, and root those ready-made, large aloe. You'll then have a bunch of plants and a neater "mother" plant as well.
By the way, please take a moment and go to your "Profile". Update your "Public Profile" by listing your location. That can be the USDA zone and/or your city/state. That way you location always shows up in the upper right hand corner. Knowing your location helps to answer many question you may post.