"Paull" in :

assume spearmint, Mentha spicata

I have a section my my yard that is covered with mint. It's an area
about 10' x 50'. I want to get rid of the stuff this fall. How can I
make sure that all the rhizomes are gone! I'd like to plant something
else there so I don't want to use chemicals that will not allow future
plants from growing there.

where are you? htey grow near stremas in central CA. else they dry out.

if wihtin an irrigated area, cardboard cover, per paghat, will kill the
patch,

you can also rip repeatedly and presistnetly wiht a digging fork,
because the underground runners are shallow.