Look into the material property alphaTest. It’s a float between 0…1 which will discard any pixel fragment below the specified alpha value (0…1 * 255) when rendering.
eg.
material.transparent = true;
material.alphaMap = texture.load( ‘…png’ )
material.depthTest = true; // ← all pixel fragments will test depth before being drawn
material.depthWrite = true; // ← all pixel fragments will update depth buffer when drawn - unless they are discarded
material.alphaTest = 0.5; // ← anything below an alpha score of 128 will be discarded.