Both keepers were untroubled in an untidy and less than exciting first half.
Both then had a decent save each to make after the break as the two sides continued to cancel each other out with neither able to find the big breakthrough, though Lucas Akins did hit the Bantams' post with 11 minutes to go.
But the afternoon ended up in frustration for the huge 8,535 crowd, though Stags preserved their unbeaten start to the campaign
With their extended injury list, the Stags side was unchanged from the midweek Carabao Cup penalty shoot-out win at Sheffield Wednesday and the home side was heartened to see injured trio Baily Cargill, James Gale and John-Joe O'Toole return to the bench.
Stags were happy to see their former striker Andy Cook, who has a habit of scoring against them, missed the game through injury.
City's deadline day recruits, Rayhaan Tulloch and Chisom Afoka were on the bench after joining on loan from West Brom and Aston Villa, respectively.
Stags forced two early corners, and from the second of them, Brunt turned the ball first time well wide.
Bradford's first real threat came on 14 minutes as Stags laboured in clearing a cross, but Brunt came up with a perfectly-timed tackle to stop Smith getting a shot at goal.
A minute later Richards was space to advance and finally sent a low shot wide from 25 yards.
And on 17 minutes Oduor tried his luck from the same distance but it was a comfortable take for Pym.
Smallwood was booked for something he said to the referee on 23 minutes.
Akins' shot on the turn on 35 minutes was deflected out as far as a throw-in as both sides struggled to create real chances.
Maris then had a shot deflect away for the home side's fifth corner kick and minutes later Akins set up Swan for a rising shot from an angle on the right that was always going over.
Mansfield successfully cleared a corner and a long throw in the one added minute to bring an uneventful first half to a goalless conclusion,
Smith forced a save out of Pym within 14 seconds of the restart as his half-volley from the right saw Pym down to his right to gather.
Walker was booked on 55 minutes for a late challenge on Maris as he cleared his lines on the edge of the home box.
Stags finally created their best chance of the afternoon on 56 minutes as Macdonald set up Keillor-Dunn for a shot from the edge of the box that Lewis had to beat away to his right.
On 64 minutes Keillor-Dunn wormed his way into the box and saw his shot blocked, the ball running to Clarke who poked just wide of the left post.
Macdonald was added to the book for a foul on 68 minutes.
The visitors made a triple chance with 20 minutes to go while Stags sent on Gale for Swan up front and straight away was booked for a foul on Stubbs, whose histrionics clearly influenced the decision.
Akins and Keillor-Dunn worked a useful ball to Gale on the left of the box, but he got his angles all wrong and it ended up looking like a pass across the box instead of a shot.
Mansfield came as close as they had all day on 79 minutes as a Macdonald corner was met b a glancing near post header by Akins that clipped the base of the far post but stayed out.
Williams replaced Clarke in the midfield for the final 10 minutes.
Gale won Stags a free kick just outside the box, but Macdonald floated it well over the crossbar.
With four added minutes looming, Williams replaced Maris for the home side.
Oyegoke was booked for sliding in on Gale just before the game ended scoreless.
STAGS: Pym, Bowery, Flint, Brunt, Macdonald, Reed, Maris (Cargill 89), Clarke (Williams 80), Keillor-Dunn, Swan (Gale 73) Akins. SUBS NOT USED: Flinders, Cooper, O'Toole, Abdullah.
BRADFORD: Lewis, Halliday, Platt, Smallwood, Walker (Tulloch 70), Osadebe (Oyegoke 80), Oduor (Pointon 60), Smith (Derbyshire 70), Stubbs, Kelly, Richards (Ridehalgh 70). SUBS NOT USED: Doyle, Afoke.
REFEREE: Leigh Doughty.
ATTENDANCE: 8,535 (1,671 away).