Which way do I go from here?

So I've been in a relationship with my now fiance for three years. He showed me a big commitment step by getting my name tattooed on his arm before the engagement, we're in a long distance relationship now since he lives across the country. He's not big in money, he lost his job & didn't care, he drove all the way here to see me...
We made love on the first night, since we haven't seen each other in over two months. The next day, he was looking at another woman's private area, the lady was wearing very short shorts & had her legs spread apart. I got angry with him & stopped talking. He asked what was wrong and I said nothing at all to him, just looked the other way.

It was now that I realize that my fiance might have anger issues.

He use to call me names a few years ago when he didn't get his way but I didn't think nothing of it, I told him I didn't like it & he hasn't called me anything until now...

So we're in his truck, he pulls into a parking lot, starts screaming at me saying things like I don't care about him & I don't love him & asking what he did wrong. But I didn't want to say anything to him because he was so furious. He puts the truck in reverse & starts driving like an idiot every time I try getting out. Then gets out of his truck slams the door & looks at me with eyes wide open, looking into mine, saying, "F-it & F-you" about 500 times.

Of course! The water works come poring out of my eyes because I am so hurt. I finally tell him & he gets in my face & is yelling that he was looking at the table in front of her, then says those hurtful words again, & chucks our engagement rings off to somewhere [which later he claimed he found. hint hint: another thing that hurt me.]

Am I that dumb? No! Of course I know he was looking at another woman with the worst intentions on his mind & it was the biggest lie! So I try walking away from him back to the beach & he keeps grabbing me & pulling me back telling me to stay with him & that I'm accusing him of things. Getting on his knees, begging me not to go.
& when he finally leaves, I go home, & there are a million texts coming in on how much he loves me & how much he's missed me. Things like what he planned for us in the future, let alone next week. Just all that sweet talk & I say "no you don't say those things to the one you love." & he apologizes a million times begging me to call him & I simply don't reply because I am stumped. I don't know what to do. I know that the more logic thing to do is to leave him...But it's so hard to drop a relationship.....?