Yes. cut the tip off down to a bud eye or point from which another cane will grow. If too much stub is left above the bud, that portion above the stub will die back
By the looks of the canes in the top two pictures, I can only presume these were packaged bareroot roses covered with wax preservative and purchased from a big box or grocery store.
Those roses commonly have a lot of harvest damage that should be pruned off prior to planting. The wax hides much of the damage and prevents it from being seen. After the wax melts off and the damaged portions are exposed, canker sets in and that portion and the cane above it dies.
In the top two pictures, cutting off the black portions of cane will destroy the new canes growing out of the good side.
Although it's unlikely, the black could stop where it is allowing the new canes to stay viable. I'd leave them as is for now and hope the new canes survive long enough to bloom. They may produce only blind growth. The two little lighter colored canes in the 2nd picture are blind growth and should be removed. They'll never produce anything and won't grow any longer.
Your only hope for the plant in the 2nd picture is that the new growth marked by the arrow will begin to grow and produce a good cane. Should that occur, I'd cut the top portion off down to a 1/4 inch above that new growth.
The bush in the top picture may stay as is. There's nothing you can do to stop it from turning black. That was going to happen no matter what you did. This is what often happens when you buy those inexpensive body bagged roses from the big box stores. They fool you and try to grow but have been damaged so much by bad harvest practices or not stored properly before shipping. These roses are usually the culls from the better growers which are sold to packagers who then pretty them up with wax to hide the damage and sell them cheap to WalMart, K Mart, Home Depot, and the other big box stores. These are the kind you'll find in 99 cent and dollar stores.
These were grade 2 roses, usually burned.

Karl's answer is perfect. Be sure to take the point about pruning just above a bud eye. These occur wherever there is or was a leaf. If there are no leaves in the area, look for a bump with a smiley line underneath it.

Thanks for Karl's detailed explanation and Michaelg's reminds. Yes, I bought them from Costco or BJ'S. Now I have learned the lessons. I thought I had bad luck with roses and was thinking to give up growing roses. Now I know I should go for the better quality resources.

The rose in the last picture was bought from David Austin. I also have other roses from them are having the black end problem now. Is this common? We had a lot of rain here in the past month. Those roses have morning sun until 1 or 2 pm I am thinking to move them to a better location by the end of summer or next spring. Are there anything I can do to avoid having the same problems again? I tried cleaning the pruner as much as I can. I do not know what else I can do to help them. Shouldn't I lay out mulch around them? Mulch retains moisture but maybe too much, perhaps?

Mulch is essential, but don't pile it around the canes-- except some do in the coldest part of winter. The graft or bud union must be protected against freezing either by planting deep (as I prefer) or mounding up.

It's timing as well as vendor quality. For best results, buy good plants. Plant bareroots in early spring (daffodil time) and potted roses in mid spring (dogwood time).

Thanks Michaelg. I wondered if the environment I provided for the roses were too humid and caused the black canes. I will definitely keep mulching around them.