Kushendra - there are no specific tools or "magic method" for removing shadows from extremely high resolution imagery within ArcGIS, but our Segmentation tools may be relatively effective at highlighting areas of shadow vs. non shadow, and allowing you to combine shaded areas into their appropriate groundcover class. (See these links to Help for Pro or ArcMap. What version are you using?)
However, I think it is worth expanding this to discuss other issues.
First, what resolution is your imagery? I'm assuming centimeters, but if you are flying high and capturing ~1 meter data, the workflow may be somewhat different.
Second and critically important, what sensor are you using? If it is a Bayer array (single CCD sensor), the spectral content of the red band includes NIR energy that cannot be completely removed, so your NDVI values will be questionable. If you are using a multi-sensor camera like frpm Micasense, TetraCam, or a hyperspectral imager (e.g. from Resonon, you should be getting good quality spectral imagery.
Third, how did you create your mosaic? If you are using a Mosaic Dataset and are rectifying each image "on the fly" into a virtual mosaic, you have not disrupted your original pixel values by resampling. Otherwise, if you have used Drone2Map, Pix4D, or similar software to create a single orthomosaic, your spectral values have already been modified by both multi-scene averaging and resampling such that an NDVI will be less accurate. (If you add this onto the Bayer array issue #2, I'd say your NDVI will be qualitative at best - not a highly accurate quantitative measurement).
All together, my experience is that NDVI dramatically reduces the effects of shadow. Since the shadow diminishes the brightness value of both the NIR and Red bands, the ratio in the NDVI should not show a dramatic difference in shadowed vs. non-shadowed regions. e.g. you may want to review this paper: "An Analysis of Shadow Effects on Spectral Vegetation Indexes Using a Ground-Based Imaging Spectromet..."
In fact, I have used NDVI specifically for the purpose of compensating for shadow. If your data seems to show dark shadows in the NDVI, I suspect your sensor is not providing good quality measurements in the two bands.
