Joining an Cutting Objects If I have two object like the two planes in the image below. 
And I join these two planes (CTRL+J). How can I cut off the part that sticks out of the bottom of the bigger plane, so this would be level on the ground, without holes. Ideally the bottom part would be one Face (or as minimal as possible). Also the internal edges/faces/vertices where the plane cut through would be ideally not be represented in the model anymore. Only the parts that you can see outside. I know I can clean it up step by step, but I was looking for a more easier, professional way. Since I would have to do this very often.
In the edit mode select the face selection mode, select the part of the mesh you want to remove, if it selects both the upper and lower parts, subdivide the selected face after its been subdivided select the part below ground level and click on P key to seperate you'll see an option that comes out click on 'selection' then you can delete the seperated Part if you want