I think those suckers were pretty THICK. For thicker suckers you should use the "Missouri pruning" method.

> Thicker suckers should not be snapped off, since could damage the whole plant .If it's thicker than a pencil, use the "Missouri pruning" method: pinch out just the tip of the sucker, leaving one or two leaves behind for photosynthesis and to protect developing fruit from sun scald.

The drawback is that suckers will develop from the stem that you leave behind, which will require additional pruning, but this technique is better when you're dealing with large suckers--if wound becomes diseased, it will be further away from the main stem, and leaving a few inches on the sucker reduces the shock to the plant.

Prune suckers all summer long to keep the plant healthy. They grow quickly, so you may need to prune once or twice a week.

I agree with Daniel.
Pruning suckers should be done early on when they are thinner than a pencil. I prune leave branches further away from the stem, leaving a few inched intact.

Well then...not much to add but I don't like people to think that their advice goes unread or unappreciated so thanks!