How to erase and reformat an old SSD drive from a Mac for using as a Time Machine?

Before my old mac went to recycling I removed the SSD drive. I have set it up as an external hard drive to use as a time machine. When I look in finder it still has the system files from the old mac. Disk utilities wont erase and format the disk and time machine wont recognise it as a disc for use an a time machine. How can I totally erase this old disk and reformat it?

[Re-Titled by Moderator]