When stretched, both DNA and RNA duplexes change their twist angles through twist-stretch coupling. The coupling is negative for DNA but positive for RNA, which is not yet completely understood. Here, our magnetic tweezers experiments show that the coupling of RNA reverses from positive to negative by multivalent cations. Combining with the previously reported tension-induced negative-to-positive coupling reversal of DNA, we propose a unified mechanism of the couplings of both RNA and DNA based on molecular dynamics simulations. Two deformation pathways are competing when stretched: shrinking the radius causes positive couplings but widening the major groove causes negative couplings. For RNA whose major groove is clamped by multivalent cations and canonical DNA, their radii shrink when stretched, thus exhibiting positive couplings. For elongated DNA whose radius already shrinks to the minimum and canonical RNA, their major grooves are widened when stretched, thus exhibiting negative couplings.