Stripe-like space target detection (SSTD) plays a key role in enhancing space situational awareness and assessing spacecraft behaviour. This domain faces three challenges: the lack of publicly available datasets, interference from stray light and stars, and the variability of stripe-like targets, which complicates pixel-level annotation. In response, we introduces `AstroStripeSet', a pioneering dataset designed for SSTD, aiming to bridge the gap in academic resources and advance research in SSTD. Furthermore, we propose a novel pseudo-label evolution teacher-student framework with single-point supervision. This framework starts with generating initial pseudo-labels using the zero-shot capabilities of the Segment Anything Model (SAM) in a single-point setting, and refines these labels iteratively. In our framework, the fine-tuned StripeSAM serves as the teacher and the newly developed StripeNet as the student, consistently improving segmentation performance by improving the quality of pseudo-labels. We also introduce `GeoDice', a new loss function customized for the linear characteristics of stripe-like targets. Extensive experiments show that the performance of our approach matches fully supervised methods on all evaluation metrics, establishing a new state-of-the-art (SOTA) benchmark. Our dataset and code will be made publicly available.