2004 Mazda M3 grinding sounds

My auto is making grinding sounds at first-slow speed until it excellerates. It has 70,000+ miles.
What could this be? What should-could be done for this concern.

Going straight, turning? Only when moving?

When was the transmission fluid and filter last service?
Have you checked the transmission fluid level?
Does the fluid smell burnt?
Are you sure it’s not a wheel bearing noise?

Above good comments. I’ll add if this is a front wheel drive, around 60K is where CV joints start to be problematic in some cars. Suggest to have your mechanic check the CV joints. Even if he doesn’t have time at that moment to put the car on a lift, he can at least look under there with a flashlight, see if the CV boot is split.

Not the CV joint? If this noise happens even when you are coasting in neutral at a slow speed, like in a parking lot, a malfunctioning brake could cause it.