To cut back is to trim something that's growing, like your front lawn or the crazy vines on the side of your house. You can even cut back on your spending, if it's out of control.
You can cut back your rose bush, and you can also cut back on the amount of money you spend, or reduce it. When someone curbs or restricts, it cuts back: "My coach cut back on the amount of time I spend on the field." The verb cut probably comes from a Germanic root also meaning "to cut," and it's related to both the Swedish kuta and the Old Norse kuti, both meaning "knife."