Open the Snipping Tool app.
Click the 3 dots at the top right of that app and select Settings.
In that apps settings disable the option to automatically save the screenshots.
Then close that app.
To take a screenshot without saving it, use the Windows Key + Shift + S keyboard combination.
That will take the screenshot and put it on the clipboard so you can then paste it inti an app and it will not save the screenshot to a file automatically.