do these regrow like the reg min roses
If you're talking about after dead heading, yes, all roses regrow but not all roses rebloom. There are some roses that will only bloom once per growing season.
If you are talking about a rose that has died down to the ground it depends on the type of rose and whether or not it's grafted or own root.
Seil, Unless they are true minis or minifloras cause they are on their own roots! I had to cut my minis to the ground this year. They are growing great and boy did they bloom hard this year!