Even though dachshunds are close to the ground with their short legs and long bodies, they can climb stairs. Of course, this may not happen immediately, as some doxies can be a little scared to try.
Installing a doggy gate is maybe the most effective way to stop them from going up or down the stairs. Another such gate may be of use upstairs to prevent them from going down.
To answer the question: can miniature dachshunds climb stairs, we have to consider more than just capability. Yes, dachshunds can go up the stairs, and training can help them be confident in doing so.