Remove all files with particular name but different extensions at once

Unix does not have file-name-extensions, nor does Microsoft's Windows (not after Windows ME. However file-explorer still has the concept). What you need to do is find all files starting with ... (in your case starting with cheatsheetold..

You can do this with cheatsheetold.*. It will then pass the file list to rm. You can use it with any command. It is not an rm thing.

Practice with echo cheatsheetold.*

It was not stated in which shell (bash, fish, zsh, csh) you desire to use some sort of wildcard when removing files.

As bash is a prominent shell I state that it would be possible to simply use this command:

rm -- cheatsheetold.*

note that the wildcard * is used after the -- as to avoid any unindented mishaps by bash shell extensions

the command line env | grep 'SHELL' might show you the shell you use. I have also tested the command line in the more POSIX reduced dash shell.

I simply do not use any other shells (like csh and tsh or fish) so I cannot tell how globbing works there.

another way to get an idea which shell is running might be this ps -p $$ where the $$ should be the PID of the current process (the shell) and ps the tool to list processes limited to the PID of the current shell.

https://help.ubuntu.com/community/ShellGlobbing