Online dynamic security assessment provides the real-time situational awareness for assessing the impact of various N-k contingencies, so that appropriate preventive/corrective controls could be armed in a timely fashion. This task is challenging due to the large number of possible contingencies, the massive scale of power systems, and the multi-scale dynamics that occur under varying operating conditions. In this study, a data mining framework for online dynamic security assessment using decision trees and a boosting technique is developed, with the following multi-stage processing. 1) In the offline training stage, classifiers consisting of multiple simple decision trees are built based on a given collection of training data, and an iterative algorithm is used to "boost" the accuracy of the classifiers. 2) In the near real-time update stage, the simple decision trees together with their voting weights are updated when new data are available, enabling a smooth tracking of the changes of decision regions. 3) In the online DSA stage, real-time phasor measurements are used to locate the current operating condition into a decision region and obtain timely security decisions. The clustering of contingencies and data preprocessing via dimension reduction of the attributes are also discussed. Numerical testing based on a practical power system demonstrates that the proposed approach works well under a variety of realistic operating conditions.