The best thing to chop ice with is an ice chisel or if you want crushed ice you can use a Lewis bag as well and a mallet to pound the ice and break it up.
You can also use a blender to chop up ice as well.
You can also by an ice chopper that crushes and chops up ice using a blade and a motor.
Ice choppers can be bought for around $20.00 to $60.00 on Amazon.com or other online stores.
Ice choppers come in manual versions which are cheaper and electric versions which are more costly but work much better and faster.
I have a Zeny Ice Crusher Machine which is also sold as an electric snow cone maker but it can simply be used to crush up ice for other things as well.
It has worked perfectly for me.
Before that I would use a mallet and a Lewis bag to crush up and chop my ice.