Q:

Read a SciFi book called THE ALTER EGO in 1960 but can't find it

I read this book in the 1960s. It was about someone who was killed. But people's minds were 'backed up' and recorded. So when you are reconstructed, your mind is restored from your latest backup. Of course you don't remember what happened. The name of the book I'm pretty sure was THE ALTER EGO. It had a light colored cover and  had a modern art line drawing of a face looking to the side.
The movie THE 6TH DAY had some of the ideas in this book.

A:

The Altered Ego by Jerry Sohl. It was published in 1954, and this cover matches your description:

Here is a review from The Magazine of Fantasy and Science Fiction, September 1954 (available at the Internet Archive):

Jerry Sohl's THE ALTERED EGO (Rinehart, $2.50) is a sort of mystery melodrama dealing with subversive efforts to tamper with our country's program to "restore" key men after death by inserting personality-recordings into their revivified bodies. It's almost rational . . . as Sohl novels go.

Here is the back cover blurb from the paperback reprint:

WHAT WILL LIFE BE LIKE IN 2045?
Chances are you'll be a
  "stab"—a stable personality.
  Science will have made it
  impossible for most men to
  commit a violent act.
You'll hope for "restoration."
  No matter how you die—
  they can bring you back to life.
  But only 200 Americans are
  "restored" each year.
If you're due for restoration,
  they'll "record" your brain.
  They'll preserve forever any
  thought you've ever had,
  any skills, any memories.
And you may have to pit your
  life against them!

