Place first 5 ingredients in a food processor or blender; process until smooth. Add feta, black beans, cilantro, and sauce; pulse 4 or 5 times or until combined.
Spread 1 1/2 tablespoons bean mixture over each tortilla; top each with 1/3 cup lettuce. Divide jicama and remaining ingredients evenly among tortillas; roll up. Cut each wrap in half diagonally.