I've never had a reason to clear the search data, so I'm uncertain what might work. Here are a few things to try.
First, make sure the actual items the search is turing up are already deleted. Otherwise turning search back on will only re-index them. You may have to go to your Mail provider's site and empty the trash and/or spam folders there.
1) Go to Settings > General > Spotlight Search and turn off Mail and/or any other items you don't want searched. Now restart and/or reset the iPad (instructions below). Turn the Spotlight Search item(s) back on and see if the problem is still there.
Or you could just leave Spotlight off, if you don't normally use it anyway.
2) Go to Settings > General > Reset and Reset All Settings. This won't delete anything off the iPad or change account information/settings, but it will return most other settings to their default. In theory, that 'might' clear some of the data like the keyboard dictionary and Spotlight catches. No idea, but if you're desperate it's worth a try. Expect to have to go through most of your settings and re-tweak things back to how you like them.
I don't have much hope for either of these solutions. A Google search shows several articles about Spotlight keeping older email messages indexed, and no solution. It's seems to only be a problem is your email account is POP (a type of protocol your email provider uses).
3) That said, my next suggestion is to delete that account form the iPad, the do the restart/rest thing before adding it again. You might want to check with your Mail ISP and see if they offer IMAP or Exchange mail service and use that setup instead.
4) In the end, the only thing that is guaranteed to work is to restore the iPad, either through iTunes on a computer or by using Settings > General > Reset > Erase all Content and Settings. If you do this you'll basically be starting with a fresh iPad. Choosing to restore a backup may or may not restore the Spotlight catche as well, so you can try the backup first and if it does not work, try it clean.
Restoring your iPad is a bit drastic. Make sure everything you want (other than iStore content like; music, apps, books, etc.) has been saved off the iPad either to a computer or the cloud. Don't trust the backup. Even when it works not all content you expect to be backed up is.
And that's all I can think of. Good luck.
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The usual fixes:
When you have problems with an app it's a good idea to clear it from RAM.
Close/Clear the app: With the problem app closed, double tap on the Home button to get the multitask bar. Tap and hold on any icon in the bar until they jiggle, then tap the minus sign on the problem app. This will remove it from RAM and insure a clean start the next time you launch the app.
If that does not work try a restart,
Restart: Hold down the power button until the power off slider appears. Slide it off. When the iPad finishes shutting down, hold down the power button again until the Apple logo appears. Apple recommends you restart the iPad at least once a month.
and then a reset if that does not work.
Reset: Hold down the power and home buttons until the Apple logo appears. The iPad will reboot. This usually takes a bit longer than a restart.
Reset All Settings: Another, somewhat more drastic thing you can do is Reset All Settings. You'll find this under Settings > General > Reset > Reset All Settings. It won't erase any of your content, apps, or accounts; but you will have to go through most of your other settings and re-tweak them back to your liking.
