Background/Objectives: There are few data about the ischemic risks induced by the large orthodontic forces during periodontal breakdown in dental pulp and neuro-vascular bundle (NVB) and none on the individual tissular stress distribution, despite their great importance for orthodontic treatment planning. Our aim was to assess, by a numerical analysis, the biomechanical behavior of dental pulp and the NVB during a simulated horizontal periodontal breakdown (1–8 mm), under 2–4 N of applied orthodontic forces and five movements (rotation, translation, tipping, intrusion, and extrusion). Additionally, the ischemic and degenerative-resorptive risks were assessed. Methods: The analysis involved 72 3D models of nine patients, totaling 720 simulations. The models were CBCT-based, having the second lower premolar and surrounding periodontium, and they suffered 1 mm of gradual horizontal periodontal breakdown (up to 8 mm loss). Results: Both forces displayed a similar qualitative stress distribution in all five movements, but with a quantitative increase (doubling of stress amounts for 4 N when compared with 2 N). The highest amounts of stress were displayed at 8 mm of periodontal loss, which is lower than the 16 KPa of the maximum hydrostatic pressure. The NVB stress was higher than the pulpal stress. Rotation was the most stressful, closely followed by tipping, intrusion, and extrusion. Conclusions: A total of 4 N of applied force seems to not induce any ischemic or degenerative-resorptive risks for healthy intact teeth, in up to 8 mm of periodontal breakdown. Intrusion and extrusion determined the highest visible tissular deformation in the NVB, with potential ischemic and resorptive-generative risks for previously traumatized/injured teeth (i.e., occlusal trauma). Rotation and translation (in particular) showed the highest coronal and radicular pulpal stress with potential ischemic and resorptive-generative risks for previously injured/traumatized dental pulp (i.e., direct-indirect pulp capping). It seems that 4 mm of periodontal breakdown could signal a clinical stress increase with potential ischemic and degenerative-resorptive risks for the previously traumatized/injured tissues.