The red look to the foliage leads me to believe you have a Cordyline (maybe the variety Red Star) not a yucca. These spiky plants are not as hardy as yucca plants but you can prune off the lowest broken leaves close to the stem to tidy up the plant. Do not cut the top of the plant as this is where new growth will come. There are many new and exciting varieties of Cordyline some very tropical like the Ti plant and some more cold hardy but they all need frost protection or can be enjoyed as houseplants. You can also remove any side baby plants growing out from the base to keep the Mother plant more symmetrical.   The baby plants can be potted up and may be more attractive than an overgrown Cordyline with wind damage. Keep growing, Marianne Binetti