With globalization and cultural exchange around the globe, most of the population gained knowledge of at least two languages. The bilingual user base on the Social Media Platform (SMP) has significantly contributed to the popularity of code-mixing. However, apart from multiple vital uses, SMP also suffer with abusive text content. Identifying abusive instances for a single language is a challenging task, and even more challenging for code-mix. The abusive posts detection problem is more complicated than it seems due to its unseemly, noisy data and uncertain context. To analyze these contents, the research community needs an appropriate dataset. A small dataset is not a suitable sample for the research work. In this paper, we have analyzed the dimensions of Devanagari-Roman code-mix in short noisy text. We have also discussed the challenges of abusive instances. We have proposed a cost-effective methodology with 20.38% relevancy score to collect and annotate the code-mix abusive text instances. Our dataset is eight times to the related state-of-the-art dataset. Our dataset ensures the balance with 55.81% instances in the abusive class and 44.19% in the non-abusive class. We have also conducted experiments to verify the usefulness of the dataset. We have performed experiments with traditional machine learning techniques, traditional neural network architecture, recurrent neural network architectures, and pre-trained Large Language Model (LLM). From our experiments, we have observed the suitability of the dataset for further scientific work.