You might want to spin down your samples to enrich for white blood cells. Erythrocytes don't have mitochondria.

You will need to purify the intact mitochondria from the other cellular debris. Check Methods in Enzymology, I believe there is an Ultracentrifuge gradient method to do this with high efficiency. Of course, you need an ultracentrifuge.

Lymphocytes from whole blood were separated by lysing the red blood cells (RBCs) using a hypotonic buffer (ammonium bicarbonate and ammonium chloride; Himedia) with minimal lysing effect on lymphocytes. Three volumes of RBC lysis buffer was added to blood sample and mixed by vortexing and inverting thoroughly for 5 min and centrifuged (Eppendorf 5415R) at 20,00 g for 10 min. The supernatant was mostly discarded, leaving behind ∼1 ml to prevent loss of cells. To the pellet, 3 vol RBC lysis buffer was added, and vortexing, inverting, and centrifuging steps were repeated two to three times until a clear supernatant and a clean white pellet were obtained. After the final wash, the supernatant was discarded completely, and the pellet was resuspended in 500 μl PBS, followed by addition of 400 μl cell lysis buffer (10 mM Tris-HCl, 10 mM EDTA, 50 mM NaCl, 10% SDS, pH 7.5) and 10 μl proteinase K (10 mg/ml stock; Himedia). The sample was vortexed to dissolve the pellet completely and incubated for 2 h at 56°C in a water bath (CW-30G; Jeio Tech) for lysis. An equal volume of phenol (equilibrated with Tris, pH 8) was subsequently added to the tube and mixed well by inverting for 1 min. The tube was centrifuged at 10,000 g (at 4°C) for 10 min, and the aqueous upper layer was transferred to a fresh tube containing equal volumes (1:1) of phenol and chloroform:isoamyl alcohol (24:1). The tube was mixed by inverting for 1 min and centrifuged for 10 min at 10,000 g (at 4°C). The supernatant was then transferred to a fresh tube, and 10 μl of 10 mg/ml RNase A (Fermentas, Thermo Scientific) was added.

The sample was incubated at 37°C for 30 min before an equal volume of chloroform: isoamyl alcohol (24:1) was added and mixed by inverting the tube for 1 min and centrifuging at 10,000 g (at 4°C) for 10 min. The supernatant was transferred to a fresh tube, and twice the volume of absolute alcohol (Merck) was added and inverted gently a few times and chilled at −20°C, followed by centrifugation at 10,000 g at (4°C) for 20 min. The supernatant was discarded, 250 μl 70% ethanol was added, and the pellet was tapped gently, followed by centrifugation at 10,000 rpm for 10 min and decanting the supernatant gently. The pellet was air-dried in a laminar air flow, and the dried pellet was resuspended in 50 μl nuclease-free water or 1× TE buffer and frozen at −20°C or −80°C for storage.

Ghatak, S., Muthukumaran, R.B. and Nachimuthu, S.K., 2013. A simple method of genomic DNA extraction from human samples for PCR-RFLP analysis. Journal of biomolecular techniques: JBT, 24(4), p.224.