I can only see two ways to get this to work the way you want. Either apply the subdivision surface modifier (not optimal) or using a multi-resolution modifier, not a subdivision surface/mirror modifier combo.
Apply your Mirror Modifier. You need to do this if you want to sculpt on a mesh that is subdivided by a modifier.
Remove your subdivision surface modifier and add a multiresolution modifier to your scultping object. Press the subdivide button to increase the subdivisions. You can also scuplt on different levels of detail using the scuplt attribute. This modifier can do a lot, read up on it here or search some videos on youtube.