Becoming a lush, weeping mass of feather-like fronds, the cat palm (Chamaedorea cataractarum) grows from low, prostrate stems, making traditional branch-pruning tasks irrelevant. The only pruning required is the removal of dead and broken fronds or those that are shading and encroaching upon nearby tropical border plants. Removal of the frond is done by cutting the frond's stem at the base, as close to the stumpy trunk as possible. It is a slow-growing palm, so do not overprune it.
Look over the health and shape of the clustering cat palm. Fully dead (browned) fronds can be pulled from the plant. Determine which fronds are problematic, either too tall or encroaching upon a building or shading other nearby plants.
Grasp the frond to be removed and trace its stem downward to the point where it attaches to the stubby trunk.
Cut the frond at its base with the hand pruners. Make the cut as close to the trunk as possible, taking care to not inadvertently wound or cut other frond stems.
Pull out the cut frond from the cluster and put in the compost pile.
Repeat steps 1 through 4 as needed. Always double-check the look of the palm after you prune out a frond. This slow-growing palm will look unattractive for some time if you overprune and leave a lopsided or scraggly specimen from overpruning.