In order to solve the problem of poor accuracy of blasting vibration prediction by the traditional Sadowski empirical formula and BP neural network, a model based on the mind evolutionary algorithm (MEA) is proposed for the first time to optimize the BP neural network. The blasting demolition of a raft slab foundation of an underground garage in Shenyang City, Liaoning Province, China, is taken as a research object, and the effects of the horizontal distance between different monitoring points, demolition area, elevation difference, the maximum amount of a single section of the charge, and the horizontal angle between the measurement point and the minimum resistance line on the peak velocity of vibration are taken into account. The empirical Sadowski formula, the MEA-BP algorithm, and the GA-BP algorithm were introduced to randomly train the 40 sets of data monitored at the site and to predict the eight sets of data outside the training, respectively. The results showed that the maximum relative errors of the results predicted by the MEA-BP model, the GA-BP model, and the empirical Sadowski formula were 14.94%, 19.36%, and 22.81%, respectively, and the average relative errors were 8.88%, 10.79%, and 16.84%, respectively. The prediction results corroborate that the MEA-BP algorithm has high adaptability in blasting vibration prediction for raft foundation demolition and provides reference for the prediction of vibration peak velocity in similar blasting projects.