Deep learning based joint source-channel coding (JSCC) has demonstrated significant advancements in data reconstruction compared to separate source-channel coding (SSCC). This superiority arises from the suboptimality of SSCC when dealing with finite block-length data. Moreover, SSCC falls short in reconstructing data in a multi-user and/or multi-resolution fashion, as it only tries to satisfy the worst channel and/or the highest quality data. To overcome these limitations, we propose a novel deep learning multi-resolution JSCC framework inspired by the concept of multi-task learning (MTL). This proposed framework excels at encoding data for different resolutions through hierarchical layers and effectively decodes it by leveraging both current and past layers of encoded data. Moreover, this framework holds great potential for semantic communication, where the objective extends beyond data reconstruction to preserving specific semantic attributes throughout the communication process. These semantic features could be crucial elements such as class labels, essential for classification tasks, or other key attributes that require preservation. Within this framework, each level of encoded data can be carefully designed to retain specific data semantics. As a result, the precision of a semantic classifier can be progressively enhanced across successive layers, emphasizing the preservation of targeted semantics throughout the encoding and decoding stages. We conduct experiments on MNIST and CIFAR10 dataset. The experiment with both datasets illustrates that our proposed method is capable of surpassing the SSCC method in reconstructing data with different resolutions, enabling the extraction of semantic features with heightened confidence in successive layers. This capability is particularly advantageous for prioritizing and preserving more crucial semantic features within the datasets.