How to play minecraft splitscreen PS3?

You can't, there's no split screen on minecraft, there's only online play, you would need another console and game.

Just press start button on the second controller and you're ready to go. Supports up to four players locally.

You do need an HDMI cable but this is how to get everything working properly.

You do not need an HDMI cable, HOWEVER it is the easiest way.
If you have the composite HD cable, it will also work.
The TV or monitor that you are using must be 720 p or higher in resolution.

Do I need to be connected to the internet to be able to use split screen?

You can get spitscreen offline cuz me and my twin brother are trying to get it to work but using the hdmi. Cuz you need something to get it to play.

You can get it offline by using something it ask you to use. So it doesn't matter if it is online or offline because it might work anyway. You try because you can do anything you want to get it to work. But don't try to break it because I have a friend that done that and they had to buy a whole new ps3 or xbox. And they tried again. And it work for them. To never try to break it with a hdmi.