A fast data acquisition (DAQ) system for axion dark matter searches utilizing a microwave resonant cavity, also known as axion haloscope searches, has been developed with a two-channel digitizer that can sample 16-bit amplitudes at rates up to 180 MSamples/s. First, we realized a practical DAQ efficiency of greater than 99% for a single DAQ channel, where the DAQ process includes the online fast Fourier transforms (FFTs). Using an IQ mixer and two parallel DAQ channels, we then also implemented a software-based image rejection without losing the DAQ efficiency. This work extends our continuing effort to improve the figure of merit in axion haloscope searches, the scanning rate.