Why op amp behave like that?
The bottom distortion is trivial to explain - you appear to be running the op-amp between 8+V and ground, you have not created a virtual ground at +4V, and so the signal is naturally clipping where the op-amp has no power to drive it.

For a simple approach, add a second battery to provide a -8V rail, if using 8V batteries, and power the negative power pin of the op-amp from that. Ground stays where it is, the + of the new battery connects to it, and the - of the new battery connects to the op-amp's negative power pin (not the inverting input - the one you currently show going to ground.)

The op amp is probably also feeling somewhat abused by having the inputs driven below the negative power rail in your current circuit - most (nearly all) op-amps are not fond of having an input that exceeds the power rails.