Grasp one of the vertical stems on the rock rose and trace it back to the base of the plant. Press your fingernail gently into the stalk until you reach an area near the base that feels harder than the remaining stem. This is the woody section of the stem.
Cut the stem off approximately 1/2 inch above the woody section of the stem using pruning shears.
Cut all of the remaining rock rose stems back to the same height, using the first cut stem as a guide. Use pruning shears to make the cuts.
Rake up all of the cut stems from the ground and place them into a compost pile or the trash.