A 2k factorial design with three centrals points was considered to evaluate the effect of adding red Tara pods extract (Caesalpinia spinosa) (440–2560 µg/mL of dough water) and NaCl (0.3–1.7 g/100 g of flour) on the acrylamide (AA) and hydroxymethylfurfural (HMF) content and sensory attributes of crackers. Additionally, the best formulation, defined as that with the lowest AA and HMF content, was compared with a commercial formulation cracker. Red Tara pods extracts were obtained through conventional extraction using pure water (60 °C, 35 min). AA and HMF content were quantified by GC-MS and HPLC-DAD, respectively. The sensory evaluation was carried out using a descriptive analysis on a 10 cm non-structured linear scale. Red Tara pods extract significantly reduced (p < 0.05) the AA and HMF content, while NaCl only influenced the HMF formation. However, the sensory attributes did not significantly change (p > 0.05), excepting the violet-gray color and salty flavor, but at acceptable levels compared with the control sample. The higher the red Tara pods extract concentration (2560 µg/mL of dough water), the lower the neoformed contaminants (NFCs) content of crackers (AA: 53 µg/kg and HMF: 1236 µg/kg) when salt level was below 3 g/100 g of flour. The action of the proanthocyanidins present in the extracts which trapped the carbonyl groups of sugars probably avoided the formation of both NFCs. Contrarily, NaCl addition (from 0.3 to 1.7 g/100 g of flour) significantly increased (p < 0.05) the HMF formation (from 1236 µg/kg to 4239 µg/kg, respectively), probably through the dehydration of carbohydrates during the Maillard reaction. When explored treatments were compared with a commercial formulated cracker, the highest mitigation effect (reductions of 40% and 32% AA and HMF, respectively) was reached with the addition of 2560 µg/mL of dough water of red Tara pods extract and 0.3 g/100 g of flour of NaCl. The addition of red Tara pods extracts integrated with the control of NaCl levels mitigated the NFCs in crackers, preserving their sensory properties. Future research should be focused on scaling this mitigation technology, considering a better chemical characterization of red Tara pods extracts as well as the validation of its use as functional food ingredient.