How to Prune Chili Pepper Plants. Part of the series: Hydroponic Chili Pepper Plants. Pruning chili pepper plants involves cutting off and removing excess branches and stems. Prune chili pepper plants to encourage new growth with help from an outdoor gardening professional in this free video clip. Read more: http://www.ehow.com/video_7953540_prune-chili-pepper-plants.html