The process of clearing areas, namely demining, starts by assessing and prioritizing potential hazardous areas (i.e., desk assessment) to go under thorough investigation of experts, who confirm the risk and proceed with the mines clearance operations. This paper presents Desk-AId that supports the desk assessment phase by estimating landmine risks using geospatial data and socioeconomic information. Desk-AId uses a Geospatial AI approach specialized to landmines. The approach includes mixed data sampling strategies and context-enrichment by historical conflicts and key multi-domain facilities (e.g., buildings, roads, health sites). The proposed system addresses the issue of having only ground-truth for confirmed hazardous areas by implementing a new hard-negative data sampling strategy, where negative points are sampled in the vicinity of hazardous areas. Experiments validate Desk-Aid in two domains for landmine risk assessment: 1) country-wide, and 2) uncharted study areas). The proposed approach increases the estimation accuracies up to 92%, for different classification models such as RandomForest (RF), Feedforward Neural Networks (FNN), and Graph Neural Networks (GNN).