how to delete attachments in gmail

The Chrome extension Dittach is said to do this, but it is still unclear for me (I didn't find the answer on their website) if our emails' content and attachments - i.e. our personal data - transit via this 3rd party company's servers or not when using Dittach. As it could be potentially dangerous to open our data to a 3rd party company, I prefer not to use it, for now.

As mentioned in @IgorIschuk's answer, it is possible to remove attachments in emails (and keep the original text) by enabling IMAP in Gmail + Thunderbird, but the workflow is quite long.

Thus, here is a detailed workflow explaining how to mass remove attachments for, say, all the emails of your Gmail that have a size > 1 MB. In my case I had ~ 1050 such emails.

First enable IMAP in Gmail's Settings. Also create a Gmail label named bigattachments, and configure it to be visible from IMAP.
Install Thunderbird (tested with Thunderbird Setup 60.5.0.exe) and set up the Gmail account.
In Thunderbird, go in All mail, right click on the columns, and enable the display of the column Size. Click on the Size column header to sort all your emails by size. Then select all the emails that have a size > 1 MB, and move them (with a drag'n'drop) to the bigattachments folder.
Now create a local folder in ThunderBird named temp. Drag'n'drop to copy all the emails from bigattachments (IMAP, on distant server) to temp (local). This step can take a long time depending on the size of the data to be downloaded.
Then install the addon AttachmentExtractor Continued (the original addon AttachmentExtract doesn't work on Thunderbird 60 anymore).
Now select all the emails in the local Temp folder. Right click, select "Extract attachments", select a destination path for the attachments. Wait. Carefully check that the attachments are removed from the emails (you can check the Size column), and that they are saved in the destination path too.
Now go to Gmail's web (https://mail.google.com/mail), go to Settings, temporarily switch to Conversation mode off, Save settings. Go to the bigattachments label. Check that the number of emails here is equal to the number of emails you processed in Thunderbird. (Note: if you don't switch to Conversation mode off, you won't be able to see the right count of emails, you would get a count of conversations instead!). Now delete all these emails in the bigattachments label. This is scary the first time, but it works. Wait a few minutes, refresh Gmail web, and enjoy the change from 5 GB of 15 GB used to 1GB used :)
Go back to Thunderbird. Select all the emails in the local Temp folder. Drag'n'drop them back to the bigattachments label (IMAP). Wait for the upload.
It's done! You can check on Gmail web that the bigattachments contain the same emails, but with attachments removed. You can now do the cleanup: a) Remove this bigattachments label (removing a label doesn't delete its emails), b) Go back to Conversation view on, c) Delete the Thunderbird's Temp local folder, or even remove Thunderbird.

Notes:

For me AttachmentExtractor Continued worked for normal attachments, but not for "inline images" (even if I checked Also extract embedded 'inline' images too), maybe this feature is not working yet. I you have a solution for this, please drop a comment.
Why copy the emails to a local folder Temp, extract the attachments there, delete the original emails in Gmail, and move the content from Temp back to Gmail? This seems unnecessarily complicated, and we could think "Let's apply AttachmentExtractor Continued directly to the bigattachments IMAP folder"! Short answer: the latter doesn't work, already tested! This is due to a Thunderbird bug.
If you only have a few emails to process (less than 10), it's not necessary to install the addon AttachmentExtractor Continued. You can skip step 5 and 6, and just click on every email of the Temp folder, and click on the bottom right part of the screen (I don't remember the name of this option, maybe it's in More...), you have a Detach feature. The only drawback is that this cannot be done for multiple emails at the same time.
Don't forget to do enable "Delete the attachment from the message" in the Tools > Addon options > AttachmentExtractor menu. If not, the attachments won't be removed from the emails! I don't know which of the 3 options is the best (normal Thunderbird code vs. Delete with AE's internal routine vs. Detach with AE's internal routine; BTW does anyone know what is the difference between the 2 last ones: Delete vs. Detach?), though.