Take an African Violet...
You can pick a leaf and it can become a whole new plant -- that's asexual reproduction. Many plants can do this. Grafting is another form of it.
However, since there is also a flower, the plant can produce seeds. That's sexual, since you need both a stamen and a pistil. One produces pollen, while the other becomes an ovary. In some plants, the pollen from the stamen needs to come from another flower (or even another plant). And there are some plants that have strictly female plants (fruit producing) and strictly male plants (they sort of flower, but never produce fruit).
Since the two processes are independent of each other, a single plant can be both asexual and sexual at the same time.