Multitask learning (MTL) has recently provided significant performance improvements in supervised classification of hyperspectral images (HSIs) by incorporating shared information across multiple tasks. However, the original MTL cannot effectively exploit both local and global structures of the HSI and the class label information is not fully used. Moreover, although the mathematical morphology (MM) has attracted considerable interest in feature extraction of HSI, it remains a challenging issue to sufficiently utilize multiple morphological profiles obtained by various structuring elements (SEs). In this paper, we propose a joint sparse and low-rank MTL method with Laplacian-like regularization (termed as sllMTL) for hyperspectral classification by utilizing the three-dimensional morphological profiles (3D-MPs) features. The main steps of the proposed method are twofold. First, the 3D-MPs are extracted by the 3D-opening and 3D-closing operators. Different SEs are adopted to result in multiple 3D-MPs. Second, sllMTL is proposed for hyperspectral classification by taking the 3D-MPs as features of different tasks. In the sllMTL, joint sparse and low-rank structures are exploited to capture the task specificity and relatedness, respectively. Laplacian-like regularization is also added to make full use of the label information of training samples. Experiments on three datasets demonstrate the OA of the proposed method is at least about 2% higher than other state-of-the-art methods with very limited training samples.