Yes. You should. I have never had a successful tree past 24″ if I didn’t cut back the tree to encourage multiple branches and a thicker stem. However, I wouldn’t do it now (in the spring, when buds are forming and new growth is happening). You may be tempted now, but don’t do it. Put it on your calendar for the late summer or early fall, or whenever you can really see that the growth has slowed. I pruned this tree in July. (I tend to see the most growth on my avocado trees from March – June.) If there is a compelling reason to do it now, such as the plant is dying, or it’s very tall, but very weak and thin, then use your judgement.
Start with a clean, sharp pruner. I use a Felco Model2. Not exactly cheap, but it does a great job. I’ve had mine for 10+ years now, and it’s still going strong.
Prune the tree in such a way to leave many leaves, but prune enough above a leaf so that there are budding areas around the stem.
I really should have put this post out in the late summer, but I just couldn’t wait. My big guy, Xavier, is in bloom, and I got my mind on my ‘cados and my ‘cados on my mind! (Xavier is not the plant in the pictures above, and as beautiful as his blooms are, I haven’t seen signs of a fruit yet — he is around 5 or so years old, I think.) Due to a recent move, I got rid of a lot of plants (gave away or composted/otherwise disposed of, depending on the health of the plant, but I just pruned a few feet off Xavier to help him through the move), but Xavier is a true keeper!