Replacement Of Internal Mac Pro SSD

Backup your data now, then you can't lose it. Take it to Apple for the disk replacement.

Clone the internal disk to an external disk

http://www.newertech.com/tech_support/manuals/mac/clon_data.php

http://nyacomputing.com/how-to-create-a-bootable-clone-of-your-mac-hard-drive/

Then when you get the new internal disk you can reclone to the new internal disk.

Note that the free app SuperDuper does not clone the Recovery partition but the paid CarbonCopyCloner does

KostasTournas wrote:

Can't I do it myself ?

I don't know, can you?

Replacing the storage in the late 2013 Mac Pro is easy

http://support.apple.com/en-us/HT202881

The purpose of replacing your internal SSD is not made clear.

If it was faulty then normally you would not be able to get files off it. You would then need to contact Apple to get a replacement (if under warranty) and if you have a backup restore from that.

If your query is about replacing the original SSD with a new bigger capacity one then the steps would be to as indicated by others here, clone (copy) the contents of the original to the new one. To do this you would not only need a program to do the closing e.g. SuperDuper or Carbon Copy Cloner, but you would also need an external case for one of the SSD drives. OWC sell an SSD Upgrade Kit for the 2013 Mac Pro which not only includes a new bigger capacity SSD drive but also a USB3 case in to which you can put the old SSD drive. You can then clone from the old one to the new one.

See https://eshop.macsales.com/shop/ssd/owc/mac-pro/2013

Note: The Mac Pro 2013 uses a proprietary Apple connector for the SSD, a standard Samsung SSD will therefore not fit, you need to buy one with Apple's special connector and the ones listed via the above link have the right connector.