Paul McManus saw a straight red for violent conduct before team-mate Jonathan Smart was also dismissed for a challenge on Kris Doolan.
However, the Fifers managed to hold on to claim a point.
East Fife: Brown, Alan Lowing, Muir, Smart, Ovenstone, McCunnie, Cargill (Conway 71), Young, Linn (Murdoch 88), McManus, Crawford (Robert Campbell 88). Subs Not Used: Baillie, Kerr.
Sent Off: McManus (77), Smart (90).
Booked: Crawford.
Goals: Cargill 64.
Clyde: Reidford, Park, Kinniburgh, Patrick Boyle, Neil McGowan, White, Gramovics, McLachlan, Strachan, John Stewart (Sawyers 70), Doolan. Subs Not Used: Allan, Stevenson, Cassidy, Lang.
Booked: Kinniburgh, Patrick Boyle.
Goals: Park 45.
Att: 463
Ref: N Watters
Source: BBC Sport
Source: BBC Sport