Yes, correct. We do now have primocane fruiting blackberries that fruit twice, like fall bearing raspberries. But most do not. Yes cut to the ground. Yes the new canes (primocanes) will be floricanes next year and fruit.

OK, seems the last of the season's berries gone so while I can still see where the berries were this year, I cut that cane to the ground. The 'new' canes will come up again from the root/spot/cut area where I cut the old cane... or from an entirely new area? I guess 'new' canes will be slimmer than the older bearing ones from the past year? I may just cut ALL back one time & then go from there to determine carefully all new canes each year ! Thanks for your patience with my ??'s but I was SO confused as to 'which cane was what' !!! I can see that those canes/roots could really take over a property if left to Nature!! Sure nice to see all the baggies of blackberries in the freezer now! One 'poster' mentioned that blackberries were the sweetest if picked when black but a few days later when the black color became a bit dull; I found that to be seemingly true ... and so do the birds !!!!

By this time of year you should have new canes already growing. They come from the crown, and come up in the general area where the crown is. Sometimes suckers form and new crowns are formed also.
Unless you have the primocane fruting type?? Then you do not want to cut the canes down as they will fruit again. One way to tell is new canes fruit from the upper 1/3 only. Then the next year fruit from the lower 2/3's of the cane.
Yeah some it's hard to tell what cane is what. If you have regular floricane fruiting blackberries. Now is a good time to cut them as you see which had berries, and which did not.