I don't think there is any native way or Solution but when when I done some search I found a Idea mass delete picklist values (setup).Which you can vote.
There I also found a Solution(Hack) which you can use in your use case.
From the original Answer.
There is an extension in Google Chrome called "Snap Links Lite." It is
a great tool (I use daily anyways). Essentially it allows you to hold
right click on the mouse and drag a select box over anything that
contains a hyperlink. So, if there are 10 hyperlinks that you want
opened in new tabs, instead of manually clicking "open in new tab"
this select box will open them for you.
Now, if we use this select box on the "Del" hyperlink of the picklist
values, it opens another tab (and for whatever reason overrides the
"are you sure" dialog box), and when the original screen is refreshed
the picklist values are deleted! All you have to do then is close the
tabs opened with snap links. I deleted 40 values in 15 seconds.
Many user successfully use it. Here is a extension link for your help. Which you can try.
Snap Links Lite