Yes, you can cut them back to the base of the plant. The general rule of thumb is that if the stems have not leafed out by mid to late May, they are most likely dead.

Well they do have some leaves growing 3/4 of the way down the stem. Can I cut it right above the new growth?

You can wait until late May and -if you are near the border with Canada or in Canada- wait until early June. Then prune them all the way down if they have not leafed out or very carefully do a scratch test to see if you see "green" on the stem.

Some of those stems can be surprisingly tricky so by waiting until then, you are giving them a last chance.

For example, I had one stem that leafed out in multiple places and looked very healthy. Then the top pair of leaves died, probably from winter issues. The stem was still green so I waited. It then started browning out so I did the scratch test and there was still green underneath. But it fizzled and died so, I cut the top few inches that were browned out (there were leaves below that part of the stem and I kept those).

Then there are stems that just fail to leaf out completely. Because leaf out happens quite early here sometimes (Feb-April), I give these stems until early to mid May to leaf out. If they do not leaf out by then, I cut them all the way down because, when I waited until the end of May, none of them ever leafed out.

With time, you will get an idea of how long to wait in your area.

Yes, you can cut them to just over the new growth.

a week or so ago.. you should have looked for the topmost active new buds.. which would hav been down where your arrow is ..... and then just cut all the stuff above off .. and then kinda leveled it off if just one or two were much taller than others ...

it would have been so much easier .. without the leaves... so that you could have seen it easier ...

it take a real leap of faith in early spring.. to just do it ... i would take them down to about 3 to 6inches.. with only two or 3 active buds ...

this type of winter damage is very common in my MI ...

i also found.. that stuff that buds out too high.. ends up falling over.. and then you end up cutting them off anyway ... so why not start short in spring ...

ken