A system and a method for making a beverage from a mixture of liquid and solid particles are disclosed. The liquid and solid particles are introduced into a chamber so as to allow the liquid to infuse with the flavor or quality of the solid particles. A piston having an integrated filter is in sealed contact with the chamber, and can be vertically displaced within the chamber. When the piston is displaced downward, air is forced from below the filter and into the mixture sitting above the filter, agitating the mixture. When the piston is displaced upward, the mixture is drawn from above the filter. This separates the spent solid particles from the infused liquid, which collects in the chamber, thereby making the beverage. Also described are a driving mechanism for displacing the piston, a dispensing mechanism for releasing the beverage, and a wiping mechanism for wiping spent solid particles.