Tropical cyclones, one of the most extreme and destructive meteorological incidents, cause extensive damage to lives and livelihoods worldwide. This study utilized remotely sensed data along with multi-criteria decision-making, geospatial techniques, and major cyclonic events Aila, Amphan, and Yaas to identify the changes in the vulnerability of cyclone-induced floods in the 19 community development blocks of Indian Sundarbans in the years 2009–2010, 2020–2021, and 2021–2022 (the post-cyclonic timespan). The Sundarbans are a distinctive bioclimatic region located in a characteristic geographical setting along the West Bengal and Bangladesh coasts. In this area, several cyclonic storms had an impact between 2009 and 2022. Using the variables NDVI, MNDWI, NDMI, NDBI, BSI, and NDTI, Landsat 8 Operational Land Imager, Thermal Infrared Sensor, Resourcesat LISS-III, and AWiFS data were primarily utilized to map the cyclonic flood-effective zones in the research area. The findings indicated that the coastline, which was most impacted by tropical storms, has significant physical susceptibility to floods, as determined by the AHP-weighted overlay analysis. Significant positive relationships (p < 0.05, n = 19 administrative units) were observed between mangrove damage, NDFI, and physical flood susceptibility indicators. Mangrove damage increased with an increase in the flood index, and vice versa. To mitigate the consequences and impacts of the vulnerability of cyclonic events, subsequent flood occurrences, and mangrove damage in the Sundarbans, a ground-level implementation of disaster management plans proposed by the associated state government, integrated measures of cyclone forecasting, mangrove plantation, coastal conservation, flood preparedness, mitigation, and management by the Sundarban Development Board are appreciably recommended.