When I place an object bigger than the background, I want it to cut off by itself just like Photoshop. But in Illustrator it doesn't do that. I tried clipping mask but it doesn't do anything.
You can create a LAYER MASK of any shape and have it apply to all the other objects on that layer. In order to achieve the behaviour that you desire, the object that is being used as the clipping mask needs to be a rectangle with the same extents as the page. This rectangle needs to be the top sub layer of the layer that you want to mask. Once you have this in place, just select the LAYER (not sub layer) and hit the Make/Release Clipping Mask button at the bottom of the layers palette and you're done. The following screenshot should help to clarify: