draw a blank

The meaning is different.

1. "to draw a blank" = to be unable to do something / to be unsuccessful. It has nothing to do with memory. Here's an example of a magazine article headline :
a. Seven magnificent movies of 2014 that drew a blank at the Oscars
- in other words, which failed to win anything at the Oscars.
And from a report on the American primaries :
b. Clinton’s win, meanwhile, thwarted hopes from Sanders’ campaign for an early morale boost after the Vermont senator drew a blank in five important contests across the Midwest and the South last week.
ie Sanders was unsuccessful in five .... etc

2. "My mind is a blank / My mind went blank", on the other hand, means "I can't/couldn't remember. Eg :
a. As soon as I sat down in the exam room, my mind went blank. I couldn't remember anything I'd studied.
b. He knew he'd gone into the kitchen to get something, but he couldn't remember what it was. His mind was / had gone completely blank.

So in the sentences you quote, (1) is possible, but (2) is more likely.

Hi susan,

"I tried to remember where I put my wallet, but I drew a blank."

Does the sentence mean I can't remember where I put my wallet?
If yes, I think it has the same meaning as the example 2 I gave above. Please correct me if I'm wrong.

Thank you very much.

No - as I said : it means "but I wasn't able to ".
in this case it comes out as the same which is why both are possible. In your sentence it means I wasn't able to remember - but that's because of the context, because of what was said before - I tried to remember..... Consider:
I tried to find John's skype address but I drew a blank.
in that context it would mean : I wasn't able to find John's skype address. .
The expression itself has nothing to do with memory

Hi susan,
Thank you very much for your helpful answer.

susan53 wrote:No - as I said : it means "but I wasn't able to ".
in this case it comes out as the same which is why both are possible.

Hi susan,

Thank you for your helpful answer. I know the two expressions don't mean the same. Do you mean the two sentences can mean the same thing because of the context?

Not that the phrases "mean the same thing" but that the co-text means that the full sentences end up meaning the same thing. As I said, change the verb in the first part and you change the meaning of the full sentence. But the meaning of the individual phrases remains the same : 1. I wasn't successful 2. I couldn't remember.

Another example :

The police had been investigating the murder for 6 months, but so far had drawn a blank.

Again, nothing to do with memory.