Go toSettings>Control Centerand findAnnounce Messages.Tap the-(minus) next to the Announce Messages.
Once you remove it from the Control Center, Siri will not announce any incoming messages.
The only way to use Announce Messages with Siri is to re-enable it again using the same steps.

It will stay disabled until you turn it back on.
If you prefer, you’re free to also disable it for a specified amount of time.
Tap and hold theAnnounce Messagesicon until a menu appears.

From there you’re free to chooseMute for 1 hourorOff for the day.
If you select either option, it will reactivate the Announce Messages feature after the specified amount of time.
You may have to use the steps listed above using your iPhone.

To jump into the Control Center on your Apple Watch, swipe up from the bottom.
Then, tap theAnnounce Messages with Siriicon to turn the feature off.
Whichever option you select, Announce Messages will automatically turn back on when that time is expired.