Relax, Unwind, Take Your Strings Off
You need to take off your old strings. Do not cut your strings off! Unwind them. You need to remember there is a lot of tension placed on your neck by the strings. Think of it as a bow (as in bow and arrow) with the strings pulling hard from both ends. If you suddenly cut the strings off you are giving your bass neck a jolt by releasing all of that tension. No need to jolt your neck.
Once the string is unwrapped from the post, it may be necessary to cut off the coiled up end of the string to take it out of the bridge. This is only necessary if your strings run through a closed hole on your bridge rather than an open slot.
If this is your first time to string a bass, you may want to keep your string uncut so you can estimate where to cut the new strings. In that case, you may need to annoyingly try to straighten out the string and pull it out through the bridge hole if it doesn't have an open slot to remove the string.
Tip: Keep your old strings as spares in case you ever have a string break.
Take off all your strings in the same way. Some people like to take one off and replace it, then they do the same for each string. It's up to you. With all of them off you have better access to clean...