Instead of valves there are a series of strategically located transfer ports - intake and exhaust, cut into the sides of the cylinder wall. The ports are on opposite sides of the cylinder. The transfer ports are opened and closed by the up and down movement of the piston. The rapidly burning fuel expands and begins forcing the piston down. As it continues downward travel it starts first to uncover the exhaust ports.
Exhaust gas begins to rush out of the cylinder.
Then the intake ports are uncovered. Two stroke engines use 2 different scavenging methods, cross-scavenging and loop scavenging. Both differing designs have particular advantages. This creates a wall or column of fresh mix that sweeps across the cylinder towards the exhaust ports. As the column advances it pushes the spent exhaust gases out of the exhaust ports.