Accurate segmentation and tracking of relevant elements of the surgical scene is crucial to enable context-aware intraoperative assistance and decision making. Current solutions remain tethered to domain-specific, supervised models that rely on labeled data and required domain-specific data to adapt to new surgical scenarios and beyond predefined label categories. Recent advances in prompt-driven vision foundation models (VFM) have enabled open-set, zero-shot segmentation across heterogeneous medical images. However, dependence of these models on manual visual or textual cues restricts their deployment in introperative surgical settings. We introduce a speech-guided collaborative perception (SCOPE) framework that integrates reasoning capabilities of large language model (LLM) with perception capabilities of open-set VFMs to support on-the-fly segmentation, labeling and tracking of surgical instruments and anatomy in intraoperative video streams. A key component of this framework is a collaborative perception agent, which generates top candidates of VFM-generated segmentation and incorporates intuitive speech feedback from clinicians to guide the segmentation of surgical instruments in a natural human-machine collaboration paradigm. Afterwards, instruments themselves serve as interactive pointers to label additional elements of the surgical scene. We evaluated our proposed framework on a subset of publicly available Cataract1k dataset and an in-house ex-vivo skull-base dataset to demonstrate its potential to generate on-the-fly segmentation and tracking of surgical scene. Furthermore, we demonstrate its dynamic capabilities through a live mock ex-vivo experiment. This human-AI collaboration paradigm showcase the potential of developing adaptable, hands-free, surgeon-centric tools for dynamic operating-room environments.