A gasifier comprises an internal chamber, a slag collection region, a slag passageway, a slag breaker, and an actuator. The internal chamber comprises a main combustion region that is configured and adapted to gasify fuel. The slag collection region is located beneath the main combustion region. The slag passageway operatively connects the main combustion region to the slag collection region. The slag breaker comprises a face that is movable relative to the internal chamber. The face is configured and adapted to move within the slag passageway in a manner such that the face contacts and mechanically breaks solidified slag into chunks of solidified slag that then fall into the slag collection region. The actuator is connected to the slag breaker and is configured and adapted to move the face of the slag breaker.