We report asymmetric magnetization-reversal behavior in the exchange-biased MnAs film epitaxially grown on GaAs(001) substrate, composed of periodic stripes of ferromagnetic alpha-MnAs and antiferromagnetic beta-MnAs phases existing in a single layer. A time-resolved domain observation reveals that the magnetization reverses with a sequence of discrete jumps of a sawtooth-type domain under an applied field parallel to the field-cooling direction, while the magnetization reversal takes place via a sudden single jump under an applied field antiparallel to the field-cooling direction. The asymmetric magnetization reversal in the MnAs system is explained by considering the nonuniform local exchange-biased field, induced by the local fluctuation of the volume ratio of the beta phase.