Nick Kyrgios left court to smash two racquets in a bad-tempered Cincinnati Masters defeat by Karen Khachanov after which he called the umpire “a tool”.
He slammed two racquets on the floor in a corridor and in the third set engaged in repeated disputes with Murphy.
Russia’s Khachanov, 23, dominated the deciding set to win 6-7 (3-7) 7-6 (7-4) 6-2 and reach round three.
Khachanov, who plays Lucas Pouille in the last 16, said Kyrgios has “great talent” but “sometimes the head is not in the right place”.
Kyrgios clashed with Murphy at the Washington Open two weeks ago and also swore at the official at Queen’s in June.
During the second set in Cincinnati, Kyrgios made clear he felt the shot clock – which counts down the seconds allowed between points – was being started too early, and visibly lost composure.
He delivered an expletive-laden rant at Murphy, stating the umpire was “the worst, hands down”.
He was handed a court violation at the end of the second set, when he walked off court for less than a minute to smash two of his racquets.
When Khachanov closed out the decider, Kyrgios told Murphy he was “a tool” and chose not to shake the official’s hand.
Kyrgios, who won his sixth career ATP singles crown two weeks ago in Washington, also complained last week in Toronto in an apparent dispute over why he could not have a white towel during a match.
The world number 27 was fined in May after he kicked a bottle, threw down his racquet and hurled a chair before defaulting in the final set of a match at the Italian Open.
He was fined £13,766 for unsportsmanlike behaviour at Queen’s in June.
In 2016 he received an eight-week ban for his behaviour at the Shanghai Masters when his efforts were questioned during defeat by Mischa Zverev.