The paper presents the effects made by a fossil diesel–HRD (Hydrotreated Renewable Diesel) fuel blend containing Ethanol (E) or Biodiesel (B) on the combustion process, Indicated Thermal Efficiency (ITE), smoke, and pollutant emissions when running a turbocharged Common Rail Direct Injection (CRDI) engine under medium (50% of full load), intermediate (80% of full load), and full (100%) loads at maximum torque speed of 2000 rpm. These loads correspond to the respective Indicated Mean Effective Pressures (IMEP) of 0.75, 1.20, and 1.50 MPa, developed for the most common operation of a Diesel engine. The fuel-oxygen mass content was identically increased within the same range of 0 (E0/B0), 0.91 (E1/B1), 1.81 (E2/B2), 2.71 (E3/B3), 3.61 (E4/B4), and 4.52 wt% (E5/B5) in both E and B fuel groups. Nevertheless, these fuels still possessed the same blended cetane number value of 55.5 to extract as many scientific facts as possible about the widely differing effects caused by ethanol or biodiesel properties on the operational parameters of an engine. Both quantitative and qualitative analyses of the effects made by the combustion of the newly designed fuels with the same fuel-oxygen mass contents of various origins on the engine operational parameters were conducted comparing data between themselves and with the respective values measured with the reference (‘baseline’), oxygen-free fuel blend E0/B0 and a straight diesel to reveal the existing developing trends. The study results showed the positive influence of fuel-oxygen on the combustion process, but the fuel oxygen enrichment rate should be neither too high nor too low, but just enough to achieve complete diffusion burning and low emissions. The Maximum Heat Release Rate (HRRmax) was 3.2% (E4) or 3.6% (B3) higher and the peak in-cylinder pressure was 4.3% (E3) or 1.1% (B5) higher than the respective values the combustion of the reference fuel E0/B0 develops under full load operation. Due to the fuel-oxygen, the combustion process ended by 7.3° (E4) or 1.5° crank angle degrees (CADs) (B4) earlier in an engine cycle, the COV of IMEP decreased to as low as 1.25%, the engine efficiency (ITE) increased by 3.1% (E4) or decreased by 2.7% (B3), while NOx emissions were 21.1% (E3) or 7.3% (B4) higher for both oxygenated fuels. Smoke and CO emissions took advantage of fuel-oxygen to be 2.9 times (E4) or 32.0% (B4) lower and 4.0 (E3) or 1.8 times (B5) lower, respectively, while THC emissions were 1.5 times (E4) lower or, on the contrary, 7.7% (B4) higher than the respective values the combustion of the fuel E0/B0 produces under full load operation. It was found that the fuel composition related properties greatly affect the end of combustion, exhaust smoke, and pollutant emissions when the other key factors such as the blended cetane number and the fuel-oxygen enrichment rates are the same in both fuel groups for any engine load developed at a constant (2000 rpm) speed.