Speech-to-text translation (ST) is a cross-modal task that involves converting spoken language into text in a different language. Previous research primarily focused on enhancing speech translation by facilitating knowledge transfer from machine translation, exploring various methods to bridge the gap between speech and text modalities. Despite substantial progress made, factors in speech that are not relevant to translation content, such as timbre and rhythm, often limit the efficiency of knowledge transfer. In this paper, we conceptualize speech representation as a combination of content-agnostic and content-relevant factors. We examine the impact of content-agnostic factors on translation performance through preliminary experiments and observe a significant performance deterioration when content-agnostic perturbations are introduced to speech signals. To address this issue, we propose a **S**peech **R**epresentation **P**urification with **S**upervision **E**nhancement (SRPSE) framework, which excludes the content-agnostic components within speech representations to mitigate their negative impact on ST. Experiments on MuST-C and CoVoST-2 datasets demonstrate that SRPSE significantly improves translation performance across all translation directions in three settings and achieves preeminent performance under a *transcript-free* setting.