How do I take out grout that was used a caulk around my tub?

Bless your heart, it's a tedious process. You can use a grout saw, ( its hand powered ). Or you can use a painter's 5in1 tool. There may be a power saw for grout, not sure. Check with rental companies

That is so much work to remove grout, have you tried all the methods to clean it first.

Yikes! Who did this???? I feel for you. To combat the mold use vinegar, it will kill the mold spores until you can tackle and fix this properly.

You will need to break up the grout and remove it before you caulk. Since the grout is getting moldy, you need to make sure there are no leaks in the plumbing, and grout all the way to the wall. One alternative is to remove the grout, and apply preformed plastic caulk that fits into crevices and corners. Even that needs caulking if you don’t catch a corner just right or the adhesive doesn’t cure long enough. Don’t rush this job and you shouldn’t have to redo it for a few years. ☺️

To remove your grout, use an oscillating multi tool and a grout removal accessory. FYI, there's a product called Tec Power Grout. It has a sealant incorporated in it. it is also stain resistant. Wishing you all the best.

They make a Silicon Caulk Remover that you can buy at the hardware store, that will soften caulk. I use one of razor blade paint scrapers that is silver. https://www.dollartree.com/Tool-Bench-Hardware-Metal-Safety-Scrapers-with-5-Blades/p342495/index.pro