What you have is a freewheel , not a cassette . If you clean up some of your grease around the axle you will see 2 or 4 slots for a freewheel puller . you need one of these two puller ,
Freewheel Remover - Park Tool & Freewheel or this one
Freewheel Remover - Park Tool & Freewheel to remove it with . For learning how
Repair Help Articles - Park Tool and follow from step 2 and on . What you had torn up is the cone to the freewheel , it come off clockwise . You remove that then you will have a mess on your hands with bearings and then you need to replace the freewheel .