Graph learning is widely applied to process various complex data structures (e.g., time series) in different domains. Due to multidimensional observations and the requirement for accurate data representation, time series are usually represented in the form of multilabels. Accurately classifying multilabel time series can provide support for personalized predictions and risk assessments. It requires effectively capturing complex label relevance and overcoming imbalanced label distributions of multilabel time series. However, the existing methods are unable to model label relevance for multilabel time series or fail to fully exploit it. In addition, the existing multilabel classification balancing strategies suffer from limitations, such as disregarding label relevance, information loss, and sampling bias. This article proposes a dynamic graph attention autoencoder-based multitask (DGAAE-MT) learning framework for multilabel time series classification. It can fully and accurately model label relevance for each instance by using a dynamic graph attention-based graph autoencoder to improve multilabel classification accuracy. DGAAE-MT employs a dual-sampling strategy and cooperative training approach to improve the classification accuracy of low-frequency classes while maintaining the classification accuracy of high-frequency and mid-frequency classes. It avoids information loss and sampling bias. DGAAE-MT achieves a mean average precision (mAP) of 0.955 and an F1 score of 0.978 on a mixed medical time series dataset. It outperforms state-of-the-art works in the past two years.