Rotating machines are among the most used equipment in industrial environments. Monitoring the machine’s parameters as well as predicting its failures are crucial tasks, as they mitigate production losses and avoid severe damage to the equipment. The combined fault scenario, where more than one fault occur simultaneously with different severity levels in the rotating machines, appears frequently in industry and it has been little investigated in the literature. In order to tackle the decomposition of mixed imbalance and misalignment faults, which are the most frequent in industry, it was proposed in this paper the Improved Variable Mode Decomposition (IVMD) technique, since VMD has shown to be not effective in adequately separating combined types of faults. The proposed automatic fault detection system joins a classifier capable of distinguishing imbalance and misalignment isolated faults from combined faults, independently from the rotating speed or severity fault level, with IVMD. It was developed using Support Vector Machine (SVM) applied to the features obtained from the vibration signature. First, the SVM classifier discriminates between healthy or fault signal, which can originate from individual or combined faults, and when the fault decomposition is required, the IVMD is applied. Subsequently, a continuous range severity level is estimated, based on the vibration signal velocity, allowing the contribution of each fault individually to the overall vibration level to be observed. The obtained results reveal that the devised SVM-based algorithm presents an accuracy of 95.43% in identifying from healthy, single and mixed imbalance and misalignment faults, and the IVMD approach accurately separates the faults.