To optimize energy structure and efficiently utilize renewable energy sources, it is necessary to establish a new electrical power–gas mutual transformation virtual power plant that has low-carbon benefits. To promote the economic and low-carbon operation of a virtual power plant and reduce uncertainty regarding the use of new energy, a multi-timescale (day-ahead to intraday) optimal scheduling model is proposed. First, a basic model of a new interconnected power–gas virtual power plant (power-to-gas demand response virtual power plant, PD-VPP) was established with P2G and comprehensive demand response as the main body. Second, in response to the high volatility of new energy, a day-ahead to intraday multi-timescale collaborative operation optimization model is proposed. In the day-ahead optimization period, the next day’s internal electricity price is formulated, and the price-based demand response load is regulated in advance so as to ensure profit maximization for the virtual power plant. Based on the results of day-ahead modeling, intraday optimization was performed on the output of each distributed unit, considering the cost of the carbon emission reductions to achieve low-carbon economic dispatch with minimal operating costs. Finally, several operation scenarios are established for a simulation case analysis. The validity of the proposed model was verified via comparison.