Low-resource extractive text summarization is a vital but heavily underexplored area of research. Prior literature either focuses on abstractive text summarization or prompts a large language model (LLM) like GPT-3 directly to generate summaries. In this work, we propose MixSumm for low-resource extractive text summarization. Specifically, MixSumm prompts an open-source LLM, LLaMA-3-70b, to generate documents that mix information from multiple topics as opposed to generating documents without mixup, and then trains a summarization model on the generated dataset. We use ROUGE scores and L-Eval, a reference-free LLaMA-3-based evaluation method to measure the quality of generated summaries. We conduct extensive experiments on a challenging text summarization benchmark comprising the TweetSumm, WikiHow, and ArXiv/PubMed datasets and show that our LLM-based data augmentation framework outperforms recent prompt-based approaches for low-resource extractive summarization. Additionally, our results also demonstrate effective knowledge distillation from LLaMA-3-70b to a small BERT-based extractive summarizer.