In some pieces, there is a pedal designation along with staccato. How should this be played?
The notation here seems pretty explicit. I would simply play them as if you weren't holding the pedal down, i.e., keep your finger motion the same as it would be if there was no pedalling. Note that this is "OK". The sustain pedal is not for legato, it's for sustain; playing staccato whilst pedalling will give you a unique effect, one that appears to be desired in this instance.
You could also try half-pedalling on each staccato note. This will help it sound more like normal staccato notes without totally breaking the sustain. Use your judgment.
When Liszt wrote that music, the pedals didn't work as well as they do now, and hitting a short note with the pedal down sounded differently than holding the key down with the pedal.
I'd hold the pedal about half-way.