Philip Rooney, from Lanarkshire, was driving service 592 between London-Aberdeen when it overturned on the M4/M25 slip road around 13 months ago. Two people died soon afterwards and a third died six months later.
Mr Rooney, 48, pleaded not guilty to three counts when he appeared at Reading Magistrates' Court on Tuesday. He was bailed to appear at Oxford Crown Court on 8 September ahead of a trial on 27 October.
Christina Toner, 76, from Dundee, and Yi Di Lin, 30, a Chinese national, died in the crash while John Carruthers, 78, of Chertsey, Surrey died in hospital on 1 July.