Here are the steps we take for pruning cucumbers
When plants are less than a foot tall, we remove any flower clusters to help plants maximize foliage and photosynthesis in early growth stages. Once plants are more than a foot tall (12-16 inches) we transition to pruning suckers and leaving new flower clusters to produce fruit.
We are trellising each week, removing all suckers at each new growth point. Some suckers develop in odd places like the end of flower clusters or re-set suckers where we have already removed them. It is important to check thoroughly and remove all suckers when they are small.
Once the plant has 18-20 leaf sections we remove the bottom three-ish leaf sets each week and any diseased looking leaves. (this increases airflow and helps divert energy to new growth).
Larger suckers and leaves may need to be cut with clippers rather than popped off by hand. Our general rule of thumb is if it is bigger than a pencil, we remove it with clippers.
Use a cup of bleach water to sanitize the knife between plants to limit the spread of disease.
We typically prune cucumbers until they succumb to disease or the elements.