Can't mount or repair Transcend 1TB external HD
Try using a great app for Mac like Disk Drill, Data Rescue 4 or R Studio to recover your own data, another option is to bring it to a computer store, and they can do it for a fee, as Best Buy does for around $450-$1200. If you prefer a free way, then I recommend using TestDisk, an open source project that will help recover and perform sector by sector scan drives. 

I would just leave the drive plugged in and use one of the applications, if the drive is still able to spin (as I'm assuming it is because it will populate in disk util). In Disk Drill, you can click the settings icon beside your drive and click "deep scan". For a 4TB HDD, it takes around 3 days. It should be fine if left running for a few days, and eventually, it will allow you to mount your old drive, and transfer the files to a new drive. Docs for TestDisk are available here

Best of Luck!