Mennie dismissed Daniel Hughes LBW for 60 on the final ball of the day to leave the Blues 3/124 against at stumps after a rain-affected first day.
Intermittent rain washed out the initial five hours of Tuesday's play at Adelaide Oval.
Hughes and New South Wales’ Moises Henriques (41 not out) blunted SA's bowlers with a 75-run stand after the home side won the toss and sent the Blues in.
Redbacks quicks Mennie (2/14 from 10 overs) and Nick Winter (1/24) were the Redbacks’ two wicket-takers.
Left-arm quick Winter struck in the sixth over, trapping Nick Larkin LBW for two when the Blues opener failed to get bat on ball playing across a fullish delivery.
Hughes and Kurtis Patterson battled through a testing period with Winter, Chadd Sayers (0/40) and Mennie gaining movement through the air and off the pitch.
The NSW pair put on a 41-run partnership before Patterson, on 17, played a loose swipe to a short Mennie delivery outside off-stump and feathered an inside edge to wicketkeeper Harry Nielsen.
NSW stalwart Henriques survived a couple of close LBW shouts but soon clicked into gear, defying the conditions to score freely - his 41 runs came from 55 balls.
SA selected leg-spinner Lloyd Pope for his first-class debut and Henriques hammered the 18-year-old's first ball for four.
But Pope, who took an eight-wicket haul for Australia in an under-19 World Cup fixture last January, battled back bravely and finished with 0/26 from six overs.
The Blues had three players in Jack Edwards, Jason Sangha and allrounder Daniel Sams featuring in their first-class debuts.