We present results from multi-epoch spectral analysis of XMM-Newton and Chandra observations of the broad absorption line (BAL) quasar APM 08279+5255. Our analysis shows significant X-ray BALs in all epochs with rest-frame energies lying in the range of ~6.7-18 keV. The X-ray BALs and 0.2-10 keV continuum show significant variability on timescales as short as 3.3 days (proper time) implying a source size-scale of ~10 r _g, where r _g is the gravitational radius. We find a large gradient in the outflow velocity of the X-ray absorbers with projected outflow velocities of up to 0.76c. The maximum outflow velocity constrains the angle between the wind velocity and our line of sight to be less than ~22°. Based on our spectral analysis, we identify the following components of the outflow: (1) highly ionized X-ray absorbing material with an ionization parameter in the range of 2.9 log ξ 3.9 (the units of ξ are erg cm s^–1) and a column density of log N _H ~ 23 (the units of N _H are cm^–2) outflowing at velocities of up to 0.76c; and (2) low-ionization X-ray absorbing gas with log N _H ~ 22.8. We find a possible trend between the X-ray photon index and the maximum outflow velocity of the ionized absorber in the sense that flatter spectra appear to result in lower outflow velocities. Based on our spectral analysis of observations of APM 08279+5255 over a period of 1.2 yr (proper time), we estimate the mass-outflow rate and efficiency of the outflow to have varied between 16⁺¹² _–8 M _☉ yr^–1 to 64⁺⁶⁶ _–40 M _☉ yr^–1 and 0.18^+0.15 _–0.11 to 1.7^+1.9 _–1.2, respectively. Assuming that the outflow properties of APM 08279+5255 are a common property of most quasars at similar redshifts, our results then imply that quasar winds are massive and energetic enough to significantly influence the formation of the host galaxy, provide significant metal enrichment to the interstellar medium and intergalactic medium, and are a viable mechanism for feedback at redshifts near the peak in the number density of galaxy mergers.