How do you choke out ground cover to redo a flower bed?

You can use a recipe we use with vinegar that will not damage the soil or another spray that is also considered safe by folks that used to use roundup, it is called Tenacity. Here is our tutorial on the vinegar spray. The recipe and application is in the tutorial for weed eating cure, but it works the same as what you want. https://www.hometalk.com/diy/outdoor/pest-repeller/weed-eat-no-more-43404548

Weed Eat No More

I would dig out all the plants I wanted to save and then use Round Up spray to kill the ground cover. I would wait until it all died back and then rake out the dead plants. I would then cover the area with black landscape fabric and cover with mulch. You don't mention what kind of ground cover you want to get rid of. Some is very difficult to remove as there may be runners under ground that encourage regrowth. Bishops Weed/Snow on the Mountain is one such ground cover that is difficult to eradicate. This particular ground covers requires shielding it from any light to eradicate it. It took me 3 years to get it all out of a small garden and even now I still see signs of it wanting to grow back even though I have left the black landscape fabric in place along with the mulch!

There's really no way to know if you get it all. Landscapers use a product called total kill for best results, but you can't plant anything for 3 months.