With predatory stars, they'll basically spit out the non-digestible parts (like snail or bivalve shells) using their mouth when they're done eating the organism inside. If the organism is digested internally or externally typically depends on how easy it is for the star to swallow the organism (some bivalves, for example, are easier to digest externally for some stars, as the stars can pry the shell open, evert the stomach, and digest the bivalve - other stars can't pry the shell open, but they can swallow the bivalve whole, so they suffocate the bivalve in their stomach, then digest it once the muscles relax and open the way for the star's digestive system to reach the bivalve meat).
Edit: to add about their usual digestion - stars basically just digest what they can, leave what they can't, and excrete the waste through their skin and tube feet. The quote below is a simple explanation:
"Excretion in echinoderms is by simple diffusion of metabolic wastes (ammonia) across thin permeable regions of the body wall. A variety of gas exchange structures, including the tube feet, is found in various echinoderms."
Source:
https://biosurvey.ou.edu/Invert_manual/Echinodermata.html