Due to the complexity and difficulty of forest resource ground surveys, remote-sensing-based methods to assess forest resources and effectively plan management measures are particularly important, as they provide effective means to explore changes in forest resources over long time periods. The objective of this study was to monitor the spatiotemporal trends of the wood carbon stocks of the standing forests in the southeastern Xiaoxinganling Mountains by using Landsat remote sensing data collected between 1989 and 2021. Various remote sensing indicators for predicting carbon stocks were constructed based on the Google Earth Engine (GEE) platform. We initially used a multiple linear regression model, a deep neural network model and a convolutional neural network model for exploring the spatiotemporal trends in carbon stocks. Finally, we chose the convolutional neural network model because it provided more robust predictions on the carbon stock on a pixel-by-pixel basis and hence mapping the spatial distribution of this variable. Savitzky–Golay filter smoothing was applied to the predicted annual average carbon stock to observe the overall trend, and a spatial autocorrelation analysis was conducted. Sen’s slope and the Mann–Kendall statistical test were used to monitor the spatial trends of the carbon stocks. It was found that 59.5% of the area showed an increasing trend, while 40.5% of the area showed a decreasing trend over the past 33 years, and the future trend of carbon stock development was plotted by combining the results with the Hurst exponent.