To address challenges in demand-side management amid the burgeoning electrification and the proliferation of emerging loads like electric vehicles (EVs), this paper proposes a novel time-shiftable flexible demand (TSFD)based peer-to-peer (P2P) negawatt (nW) trading framework aimed at unleashing the potential of residential demand flexibility. Unlike the conventional demand response (DR) schemes, the proposed framework empowers residential consumers to spontaneously and actively arrange their energy usage behaviors based on dynamic market signals, providing them with higher arbitrage opportunities. A two-stage P2P nW trading model is formulated for the proposed framework. In the first stage, a comprehensive nW-oriented home energy management system (HEMS) model is introduced, integrating the intricacies of market role switching and diverse characteristics of TSFD. In the second stage, an intra-community rule-driven P2P nW trading mechanism, encompassing detailed allocation, matchmaking, and payment rules, is designed to ensure the autonomy and independence of participants and efficient market-clearing. The iterative process between the two stages enables optimal scheduling of flexible demand, changeable market roles, and bidding strategies, thereby decreasing electricity usage costs for all nW prosumers. The proposed framework is tested on a 35-node low-voltage (LV) distribution system and simulation results validate its effectiveness and superiority in improving economic benefits and managing demand within the residential community.