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We study the mechanical response of bulk CrSBr in temperature using a CrSBr string resonator. We observe two abrupt changes in eigenfrequency and quality factor of the resonator with decreasing temperature, a strong one around 140 K due to an antiferromagnetic phase transition, and a weaker one around 200 K possibly related to a change of spin correlations. We find that the antiferromagnetic transition persists through a temperature window of 30 K rather than showing a narrow sharp change, indicating a gradual spin transition process. In addition, the quality factor exhibits an unexpected increase during the transition, which violates the theoretical prediction. Finally, we demonstrate that in a CrSBr/SiN composite resonator, its vibrational state is sensitively affected by the constituent CrSBr layer during the magnetic phase transitions. It reveals the potential of a composite resonator in both controlling its vibration state with and probing phase transitions of its constituent materials. Our study not only enriches the details about the antiferromagnetic phase transition in CrSBr, but also opens up possibility in magnetic sensing and in situ tuning using composite mechanical resonators. [ABSTRACT FROM AUTHOR]