Results are reported from a joint analysis of Phase I and Phase II data from the Sudbury Neutrino Observatory. The effective electron kinetic energy threshold used is T-eff = 3.5MeV, the lowest analysis threshold yet achieved with water Cherenkov detector data. In units of 106 cm(-2) s(-1), the total flux of active-flavor neutrinos from B-8 decay in the Sun measured using the neutral current (NC) reaction of neutrinos on deuterons, with no constraint on the B-8 neutrino energy spectrum, is found to be Phi(NC) = 5.140(-0.158)(+0.160)(stat)(-0.117)(+0.132)(syst). These uncertainties are more than a factor of 2 smaller than previously published results. Also presented are the spectra of recoil electrons from the charged current reaction of neutrinos on deuterons and the elastic scattering of electrons. A fit to the Sudbury Neutrino Observatory data in which the free parameters directly describe the total B-8 neutrino flux and the energy-dependent nu(e) survival probability provides a measure of the total B-8 neutrino flux Phi(8B) = 5.046(-0.152)(+0.159)(stat)(-0.123)(+0.107)(syst). Combining these new results with results of all other solar experiments and the KamLAND reactor experiment yields best- fit values of the mixing parameters of theta(12) = 34.06(-0.84)(+1.16) degrees and Delta m(21)(2) = 7.59(-0.21)(+0.20) x 10(-5) eV(2). The global value of Phi(8B) is extracted to a precision of (+2.38)(-2.95)%. In a three-flavor analysis the best fit value of sin(2) theta(13) is 2.00(-1.63)(+2.09) x 10(-2). This implies an upper bound of sin(2) theta(13) < 0.057 (95% C.L.).