Filed 1040X right after I submitted 1040 due to mistakenly doubling the HSA contribution on 1040 but had to mail it. Have not hard anything from IRS?

[mesquitebean]

I assume you physically mailed the Form 1040X and associated changed forms yourself.  TurboTax does not mail it for you.

It can take the IRS up to 16 weeks to process an amended return.   How long has it been?

Does your amended return show up in this IRS tool?  It should show up in the tool about 3 weeks after you mailed it.
https://www.irs.gov/filing/wheres-my-amended-return

[luepher]

Yes, once I realized (cross-checking with Credit Karma) that I've made a mistake, I called Intuit and, after going through, I put in the max HSA into a field where I should not have put it, doubling the HSA contribution and resulting in penalty and reduction in the return. I was advised to file 1040X and yes, apparently it could only be filed by mail. Sent it by certified mail on 3/27, they received it. It's now been around 3 and a half months...
I was not aware of IRS Tool, thank you for that! What it shows is this:

We processed your amended return on May 24, 2019.

If you have not received a notice and you would like to speak to a customer service representative, call [phone number removed], extension 633, between the hours of 7 a.m. and 7 p.m., Monday through Friday. You will need a copy of your amended return.

I certainly have not received any notices... I take it I'll need to call them then.

[mesquitebean]

 That's been almost 7 weeks since that process date, so I'd phone them.   Also double-check what it shows for your mailing address. Good luck.

[Anonymous]

you probably filed the amended return before the IRS fully processed the original return.   this can cause delays because the original efiled return goes one route while the amended went another and now the IRS has two returns that need to be processed.  with different departments handling them.    there is also the possibility that the IRS disagrees with the original return which would change the numbers that need to be on the amended return.     in future if you need to file amended return wait til the original is fully processed which means your payment if balance due has been cashed or you received your refund.