This paper presents a deep BSDE approach for simultaneously pricing and delta-gamma hedging large portfolios of high-dimensional multi-asset Bermudan options. The authors cast the portfolio hedging problem into a framework of discretely reflected BSDEs, which naturally incorporate early exercise features. By leveraging the One Step Malliavin scheme, they derive a triple of stochastic processes corresponding to option prices, deltas, and gammas. This allows for the construction of a gamma hedging strategy that imposes second-order conditions to mitigate discrete replication errors inherent in delta hedging. The discretized system is solved using neural network regression Monte Carlo, enabling efficient handling of high-dimensional risk factors (up to 100). Numerical experiments on basket options and mixed portfolios demonstrate that the proposed method yields accurate prices and Greeks, and significantly outperforms standard delta hedging in terms of replication accuracy and PnL distribution, especially under volatile market conditions.