Raspberry seeds are a by-product of berries, both from their primary processing, such as in juice production, and secondary processing, such as in oil extraction. These seeds contain plenty of valuable components such as crude fiber, proteins, fats, and vitamins. Quality characterization is the initial step toward using these seeds as a sustainable and functional food. The aim of studying raspberry seeds’ quality profile, both before oil extraction and after different processing methods (supercritical CO2, subcritical CO2, cold pressing, and hexane solvent), is to point out the benefits of this by-product and to raise consumer awareness about their health and well-being benefits. This study provides evidence that raspberry seeds have good physical parameters for use in other products as a functional food enrichment ingredient, such as in baked goods, offering considerable health benefits due to their high nutrient content. The weights, peroxide values, moisture content, nutritional energy values, and colors were determined before oil extraction to give initial seed values. The nutrient content and amounts of macroelements, P, K, Ca, and Mg, as well as microelements, B, Zn, Cu, Fe, and Mn, were determined in the tested variety ‘Polka’, both before and after oil extractions and using different methods. The raspberry seeds’ moisture was 9.2%, their peroxide content was 5.64 mEq/kg, their nutritional value was 475.25 Kcal., and their total weight was 2.17 mg (1000 units). The seeds contain 7.4% protein, 22.1% crude fiber, 11.0% crude fat and oil, and 2.8% sugar. We determined how different oil extraction methods influence the nutrient, micro-, and macro-component values. We concluded that the seeds contained the highest manganese (45.3 mg/kg), iron (29.2 mg/kg), and zinc (17.4 mg/kg) contents and the lowest content of copper (5.1 mg/kg). This research shows that raspberry seeds represent a potential natural food ingredient, and after oil extraction with subcritical or supercritical CO2 or cold pressing, they can be used as a sustainable and functional food.