Mullen, who started the day in a share of the lead with Irishman Dunne and Kristoffer Broberg of Sweden, ended the second round at the top of the leaderboard alongside fellow Briton Anthony Wall (68).
"It's unbelievable really to be in this position in my first event as a pro, it’s the stuff you dream about," Englishman Mullen, 21, told reporters after carding a 69 at St Andrews for an 11-under-par total of 133.
"It's impossible not to think about winning but I've got to just try and take care of tomorrow and see what happens on Sunday."
Dunne shot a 70 at St Andrews, one of three courses being used in this week's pro-am event, to share third spot on 10-under with Briton Jamie Donaldson (65), Thorbjorn Olesen of Denmark (66) and American Chris Stroud (66).
The Irishman clearly has a fondness for the Home of Golf, having gone into the final round of the British Open at St Andrews in July in a tie for the lead while still an amateur.
"It's a lot different playing here this week without all the big stands at the Open," said Dunne, 22. "Jimmy’s playing just a little bit better than I am but it’s great to see him getting off to such a good start.
"I think our performances just show the high levels of the amateur game and that the guys coming through can play good enough golf to compete at professional level."
Mullen and Dunne were members of the Britain and Ireland team that beat the United States in the Walker Cup last month.
(Writing by Tony Jimenez; Editing by Toby Davis)
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