Smith, who lost to Luke Littler in the World Series of Darts Finals in Amsterdam on Sunday, was defeated 6-3 by his Welsh opponent Clayton.
Clayton jumped to an early three-leg lead in Budapest, firing off four 180s and averaging 94.17 as Smith faced a first-round exit despite a brief comeback.
Next up for Clayton is top seed and defending champion Dave Chisnall. Peter Wright narrowly defeated Joe Cullen in a deciding leg, while Raymond van Barneveld advanced with a 6-3 win over Ritchie Edhouse; he’ll take on Ross Smith on Saturday.
The annual £600,000 tournament will be held at the Mattioli Arena in Leicester from October 7-13, featuring 32 of the world’s best players vying for the prestigious title, previously won by Luke Humphries.
Humphries, who claimed his first TV ranking title last year by defeating Gerwyn Price, will return to defend his title. Six-time champion Michael van Gerwen is also set to compete, and teenage sensation Luke Littler will make his double-start debut in the East Midlands.
In a change from last year’s format, the semi-finals on October 12 will be best of nine sets, with the final on October 13 played over the best of 11 sets.