Many, many plants can be made into rope. These range from sunflower, to nettles, to jute. The process is quite complex and requires some knowledge, practice, or more expensive equipment. I have a student in another endeavor who taught herself spinning and weaving and I have had some discussions with her on this as well as this having been an interest of mine for a while.
The basic process of extracting fibers from plants additionally poses some sustainability problems if not well managed (there were significant laws passed in the Middle Ages to keep people from fowling the rivers and streams making linen) but if managed reasonably well can provide some additional nutrients for your plants.
The first step is to cut the plant, and you may want to strip the leaves to compost them separately. Next you take the stems and ferment them under fresh water until the fibers start to separate. Discard the water (perhaps onto your garden). The next step is to pound the retted stems until the fibers are separate, and then spin them into twine. I don't think that the fibers need to be combed between pounding and spinning, since they should start off parallel, but don't quote me on that. The twine can then be "plied" into rope.
Spinning either requires use of a drop spindle (which requires significant practice but the tool easy to improvise) or a spinning wheel (more maintenance, more complexity in the tool, easier use but still requires practice).
Additionally am I right that this is an annual? if so you might consider, instead of sheeting it under, seeing it as an initial temporal layer in the garden while perennials are becoming better established.