Influences of periodic mechanical deformation (PMD) on spiral breakup that results from Doppler instability in excitable media are investigated. We present a new effect: a high degree of homogeneous PMD is favored to prevent the low-excitability-induced breakup of spiral waves. The frequency and amplitude of PMD are also significant for achieving this purpose. The underlying mechanism of successful control is also discussed, which is believed to be related to the increase of the minimum temporal period of the meandering spiral when the suitable PMD is applied.