Hello Paul,

Blackberries and raspberries have biennial canes (shoots). The first year, the shoots grow very quickly but they don't generally produce flowers. These are likely the shoots that you are having issues with. Unfortunately, you cannot prune out all of these canes as your current canes will die in the fall and you won't have any canes at all. If you prune out all of these canes, the plant may die.

You can, however, do minor pruning on these canes. This could include cutting the canes as they start to bend into your yard. Attached is a publication on raising blackberries and raspberries.

Hopefully this helps!
Robby