The objective of few-shot named entity recognition is to identify named entities with limited labeled instances. Previous works have primarily focused on optimizing the traditional token-wise classification framework, while neglecting the exploration of information based on NER data characteristics. To address this issue, we propose a Multi-Task Semantic Decomposition Framework via Joint Task-specific Pre-training (MSDP) for few-shot NER. Drawing inspiration from demonstration-based and contrastive learning, we introduce two novel pre-training tasks: Demonstration-based Masked Language Modeling (MLM) and Class Contrastive Discrimination. These tasks effectively incorporate entity boundary information and enhance entity representation in Pre-trained Language Models (PLMs). In the downstream main task, we introduce a multi-task joint optimization framework with the semantic decomposing method, which facilitates the model to integrate two different semantic information for entity classification. Experimental results of two few-shot NER benchmarks demonstrate that MSDP consistently outperforms strong baselines by a large margin. Extensive analyses validate the effectiveness and generalization of MSDP.