Accurate estimation of terrestrial gross primary productivity (GPP) is essential for quantifying the carbon exchange between the atmosphere and biosphere. Light use efficiency (LUE) models are widely used to estimate GPP at different spatial scales. However, difficulties in properly determining the maximum LUE (LUEmax) and downregulation of LUEmax into actual LUE result in uncertainties in the LUE-estimated GPP. The recently developed P model, a new LUE model, captures the adaptability of vegetation to the environment and simplifies parameterization. Site-level studies have proven the superior performance of the P model over LUE models. As a representative karst region with significant changes in forest cover in Southwest China, Qiannan is useful for exploring the spatiotemporal variation in forest GPP and its response to climate change for formulating forest management policies to address climate changes, e.g., global warming. Based on remote sensing and meteorological data, this study estimated the forest ecosystem GPP in Qiannan from 2000–2020 via the P model. This study explored the spatiotemporal changes in GPP in the study region over the past 20 years, used the Hurst index to predict future development trends from a time series perspective, and used partial correlation analysis to analyse the spatiotemporal GPP changes over the past 20 years in response to three factors: temperature, precipitation, and vapor pressure deficit (VPD). Our results showed that (1) the total amount of GPP and average GPP in Qiannan over the past 21 years (2000–2020) were 1.9 × 104 ± 2.0 × 103 MgC ha−1 year−1 and 1238.9 ± 107.9 gC m−2 year−1, respectively. The forest GPP generally increased at a rate of 6.1 gC m−2 year−1 from 2000 to 2020 in Qiannan, and this increase mainly occurred in the nongrowing season. (2) From 2000 to 2020, the forest GPP in Qiannan was higher in the southeast and lower in the northwest, indicating significant spatial heterogeneity. In the future, more than 70% of regional forest GPP will experience a weak increase in nonsustainability. (3) In Qiannan, forest GPP was positively correlated with both temperature and precipitation, with partial correlation coefficients of 0.10 and 0.11, respectively. However, the positive response of GPP to precipitation was approximately 70.47%, while that to temperature was 64.05%. Precipitation had a stronger restrictive effect on GPP than did temperature in this region, and GPP exhibited a negative correlation with VPD. The results showed that an increase in VPD inhibits GPP to some extent. Under rapid global change, the P model GPP provides new GPP data for global ecology studies, and the comparison of various stress factors allows for improvement of the GPP model in the future. The results of this study will aid in understanding the dynamic processes of terrestrial carbon. These findings are helpful for estimating and predicting the carbon budget of forest ecosystems in karst regions, clarifying the regional carbon absorption capacity, clarifying the main factors limiting vegetation growth in these regions, promoting sustainable regional forestry development and serving the “dual carbon goal.” This work has important guiding significance for policy formulation to mitigate climate change.