Background: Tubulin plays a pivotal role in cell division and other essential cellular processes, making it a key pharmacological target for cancer therapy, antiparasitic treatments, and neurodegenerative diseases. Numerous compounds have been developed to regulate microtubule polymerization through tubulin binding; however, most have shown significant limitations, including adverse side effects, poor bioavailability and limited specificity. In recent years, peptide-based therapies have gained considerable attention, particularly for their ability to modulate protein–protein interaction while offering improved selectivity and safety profiles. Methods: In this study, we employed an integrated computational–experimental approach combining molecular docking, molecular dynamics simulations, and MM-GBSA free energy calculations to design and evaluate 14 peptides derived from the αβ-tubulin dimer interface. Results: The peptide NH2-P14-COOH emerged as the most promising candidate, displaying the stronger inhibition of tubulin polymerization activity (IC50 = 11.24 ± 3.82 μM), selective cytotoxicity against NCI-H1299 lung carcinoma cells (IC50 = 45.64 ± 3.20 μM), and no significant toxicity toward non-cancerous EA.hy926 endothelial cells (IC50 > 100 μM). Flow cytometry analysis confirmed that NH2-P14-COOH induces apoptosis, supporting a mechanism of action based on microtubule disruption. Conclusions: These findings highlight NH2-P14-COOH as a selective antimitotic peptide with a favorable therapeutic index and demonstrate the potential of structure-guided peptide design for the development of novel microtubule-targeting agents with reduced off-target toxicity.