Administering preoperative radiochemotherapy (RCT) in stage II-III tumors to locally advanced rectal carcinoma patients has proved to be effective in a high percentage of cases. Despite this, 20–30% of patients show no response or even disease progression. At present, preoperative response is assessed by a combination of imaging and tumor regression on histopathology, but recent studies suggest that various genetic abnormalities may be associated with the sensitivity or resistance of rectal cancer tumor cells to neoadjuvant therapy. In the present study we investigated the relationship between genetic lesions detected by high-density single-nucleotide polymorphisms (SNP) arrays 6.0 and response to neoadjuvant RCT, evaluated according to Dworak criteria in 39 rectal cancer tumors before treatment. The highest frequency of copy-number (CN) losses detected corresponded to chromosomes 18q (n = 27; 69%), 1p (n = 22; 56%), 15q (n = 19; 49%), 8p (n = 18; 48%), 4q (n = 17; 46%), and 22q (n = 17; 46%); in turn, CN gains more frequently involved chromosomes 20p (n = 22; 56%), 8p (n = 20; 51%), and 15q (n = 16; 41%). There was a significant association between alterations in the 1p, 3q, 7q, 12p, 17q, 20p, and 22q chromosomal regions and the degree of response to therapy prior to surgery. However, 4q, 15q11.1, and 15q14 chromosomal region alterations were identified as important by five prediction algorithms, i.e., those with the greatest influence on predicting the tumor response to treatment with preoperative RCT. Multivariate analysis of prognostic factors showed that gains on 15q11.1 and carcinoembryonic antigen (CEA) levels serum at diagnosis were the only independent variables predicting disease-free survival (DFS). Lymph node involvement also showed a prognostic impact on overall survival (OS) in the multivariate analysis. A deep-learning-based algorithm showed a 100% success rate in predicting both DFS and OS at 60 months after diagnosis of the disease. In summary, our results indicate the existence of an association between tumor genetic abnormalities at diagnosis, response to neoadjuvant therapy, and survival of patients with locally advanced rectal cancer. In addition to the clinical and biological characteristics of locally advanced rectal cancer patients, these could be used in the future as therapeutic and prognostic biomarkers, to identify patients sensitive or resistant to preoperative treatment, helping guide therapeutic decision-making. Additional prospective studies in larger series of patients are required to confirm the clinical utility of the newly identified biomarkers.