Three new heterometallic complexes with formulas of [Dy(III)2Co(III)2(OMe)2(teaH)2(acac)4(NO3)2] (1), [Dy(III)2Co(III)2(OH)2(teaH)2(acac)4(NO3)2]·4H2O (2), and [Dy(III)2Co(III)2(OMe)2(mdea)2(acac)4(NO3)2] (3) were characterized by single-crystal X-ray diffraction and by dc and ac magnetic susceptibility measurements. All three complexes have an identical "butterfly"-type metallic core that consists of two Dy(III) ions occupying the "body" position and two diamagnetic low-spin Co(III) ions occupying the outer "wing-tips". Each complex displays single-molecule magnet (SMM) behavior in zero applied magnetic field, with thermally activated anisotropy barriers of 27, 28, and 38 K above 7.5 K for 1-3, respectively, as well as observing a temperature-independent mechanism of relaxation below 5 K for 1 and 2 and at 3 K for 3, indicating fast quantum tunneling of magnetization (QTM). A second, faster thermally activated relaxation mechanism may also be active under a zero applied dc field as derived from the Cole-Cole data. Interestingly, these complexes demonstrate further relaxation modes that are strongly dependent upon the application of a static dc magnetic field. Dilution experiments that were performed on 1, in the {Y(III)2Co(III)2} diamagnetic analog, show that the slow magnetic relaxation is of a single-ion origin, but it was found that the neighboring ion also plays an important role in the overall relaxation dynamics.