Unwanted features can be annoying. Your device should be set to your liking. Lets get this fixed. When did this issue start? Does the device play the entire message or just an alert that a new message is available? Send details.
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Page 95 of your user manual: http://cache.vzw.com/multimedia/mim/samsung-gusto-3/basic-samsung-gusto-3-ug.pdf
Text Message Readout
1. From the Home screen, press the Left Soft Key Menu ➔ Settings ➔ Accessibility ➔ TXT Message Readout.
2. Choose On or Off to enable or disable the Readout option for text messages.