This paper presents the experimental realization of an ultrafast electron microscope operating at a repetition rate of 75 MHz based on a single compact resonant microwave cavity operating in a dual mode. This elliptical cavity supports two orthogonal TM110 modes with different resonance frequencies that are driven independently. The microwave signals used to drive the two cavity modes are generated from higher harmonics of the same Ti:Sapphire laser oscillator. Therefore, the modes are accurately phase-locked, resulting in periodic transverse deflection of electrons described by a Lissajous pattern. By sending the periodically deflected beam through an aperture, ultrashort electron pulses are created at a repetition rate of 75 MHz. Electron pulses with τ = (750 ± 10) fs pulse duration are created with only (2.4 ± 0.1) W of microwave input power; with normalized rms emittances of ϵn,x = (2.1 ± 0.2) pm rad and ϵn,y = (1.3 ± 0.2) pm rad for a peak current of Ip = (0.4 ± 0.1) nA. This corresponds to an rms normalized peak brightness of B n p , rms = ( 7 ± 1 ) × 10 6 A/m2 sr V, equal to previous measurements for the continuous beam. In addition, the FWHM energy spread of ΔU = (0.90 ± 0.05) eV is also unaffected by the dual mode cavity. This allows for ultrafast pump-probe experiments at the same spatial resolution of the original TEM in which a 75 MHz Ti:Sapphire oscillator can be used for exciting the sample. Moreover, the dual mode cavity can be used as a streak camera or time-of-flight electron energy loss spectroscopy detector with a dynamic range >104.