Bloodstream infections caused by carbapenem-resistant Gram-negative bacteria represent a major therapeutic challenge to clinicians worldwide. This study examined the epidemiology of carbapenem and colistin resistance in Klebsiella pneumoniae, Escherichia coli, Pseudomonas aeruginosa, and Acinetobacter baumannii blood isolates in an academic institution in Oman. Adult patients with bloodstream infections caused by Klebsiella pneumoniae, Escherichia coli, Pseudomonas aeruginosa, and Acinetobacter baumannii, between January 1, 2017, and December 31, 2020, were identified. Rates of carbapenem resistance, carbapenem-colistin dual resistance, and 30-day all-cause mortality were examined. 585 non-repeat bloodstream infections due to Klebsiella pneumoniae, Escherichia coli, Pseudomonas aeruginosa, and Acinetobacter baumannii were identified during the study period. OXA-48 was the most prevalent carbapenemase gene in carbapenem-resistant K. pneumoniae blood isolates. Carbapenem resistance was observed in 160 (27.7%) of blood isolates, with 131 (81.9%) of these being healthcare-onset cases. Carbapenem resistance was highest in Acinetobacter baumannii (80.4%), followed by Klebsiella pneumoniae (46.4%), and Pseudomonas aeruginosa (29.9%). Sixteen (13.4%) of the carbapenem-resistant blood isolates were found to be colistin resistant. Thirty-day all-cause mortality was 68.1% in patients with bloodstream infections caused by carbapenem-resistant isolates, versus 21.3% in patients with bloodstream infections caused by carbapenem-susceptible isolates. The prevalence of carbapenem resistance and carbapenem-colistin dual resistance in Gram-negative blood culture isolates from patients with bloodstream infections is unacceptably high. Patients with bloodstream infections due to carbapenem-resistant isolates had substantially higher mortality.