You cannot just remove cells from a raster. The equivalent would be to change the value of random cells to NODATA (or zero, as needed). To do this, you could create a random point layer, then convert this to raster. Once a raster, reclassify the cells to whatever value will delete the vegetation values. Make sure your other cells have some other value to keep them apart, of course. Do you have Spatial Analyst? If so, the Set Null function can be used to replace cell values where a condition is met, e.g. where your random points lie. Use this to change your vegetation cell values accordingly.