I tried using the Sen2Cor plugin within SNAP, but it does not seem that effective for cloud removal. The outputs look exactly identical. Is there any particular way how I could mask any form of cloud in the images and remove them ?
sen2cor does not remove the clouds. It is doing an atmospheric correction and masks the clouds.
You can use the scl_cloud_*_proba flags in the quality_scene_classification flag band or the value of quality_cloud_confidence to remove them on your own. For example, you can set the valid pixel expression of reflectance bands.
However, cloud masking is not perfect. If you’re not satisfied you can check if Idepix for Sentinel-2 (also not perfect) fits your needs. It does the detection on an S2 L1C prodcut.