What SM should do if QA says he is not able to understand the story at the time of execution?

Judging from your terse description, it sounds like a challenge for the development team (of which "QA guy" is probably a member... right?) and a good subject for an upcoming retrospective discussion about how to get stories "ready".

What it seems to mean to me is: if the development team does not have a good understanding of the requirements of a story, how did it get estimated and included in the plan to complete a potentially releasable increment? Note that this is not a rhetorical question, simply a question meant to inspect the process and try and find out if adaptation is required.

Does the development team consider it a problem and did they come to you for help? (And if so, what was their actual question?) Or do you consider it a problem and are you trying to tell them that they have a problem? This distinction is important for how and when a Scrum Master should act. It would also be important to know if this is an exception or a recurring pattern.

he says that he is not able to understand the Story (Requirement)

And that's it. He freezes up. :)

Can't anybody from the Scrum team ask why he doesn't understand the story and work together to clear the impediment the sooner the better?  Everyone in the team should understand that work is changing, requirements revisited and adjusted when needed and more actions are discovered as the work emerges. That happens in the middle of a sprint as well, and the team inspects and adapt so that things keep moving on towards the goal, even late in the sprint. 

Is this QA member in the team? Is he reporting issues during the daily scrum? Are these issues impediments? If so, are these impediments out of the domain resolution of the dev team?

I might be missing something from your description, but when someone in the team is not able to understand something then a conversation around it usually solves the problem.

There are two issues here.

The first is the immediate issue. There is work and it is not understood by one or more members of the Development Team. This is an impediment to ongoing work, but it can be resolved. The Product Owner should become involved to ensure that everyone fully understands the work being done, and this can be facilitated by the Scrum Master if it's necessary.

The longer term issue is two-fold. First, why was the confusion not raised much earlier? Everyone on the Scrum Team should feel safe to raise questions. Refinement and planning are the perfect opportunities to raise questions and make sure that the team has a shared understanding of the work. Second, are others are confused about the work being done or if there is also a fear of asking questions or getting clarifications? This goes back to a team dynamics and safety concern. I'd want to understand what is going on - knowing this can help identify what needs to happen to appropriately support the team.

What do we do right now to move forward? How did we get into this situation? What do we do different in the future to prevent this from happening again?   

As Scrum Master those 3 questions should be driving your actions. The first should be the easiest to deal with because there are apparently multiple other individuals on the Scrum Team that understand the story since work has been done. One or more of those individuals should be sitting with the "QA guy" right now helping him to understand so that he can act on the work.  If he is not able to understand then one of the individuals that does understand should be able to complete the work for him.  If that is not possible or individuals are unwilling then questions 2 and 3 become much bigger in scope.

When discussing questions 2 and 3 remember that you participate in the discussion as part of the team. In this case it appears that at least 1 member of the team does not fully appreciate the Scrum Values of courage and openness and fears that there will be lack of respect for him.  And if there is 1 member it is likely that there are others.  This is your domain as Scrum Master.  Part of the actions to address questions 2 and 3 will be for you to work on this.  There will be other actions as well that will fall to the rest of the Scrum Team but I feel that the values issue may be the heart of it all.

Good luck and lead by example. Sometimes difficult conversations have to occur and as facilitator you may have to venture outside of your own comfort zone to force the conversation into uncomfortable territory.

QA guy not raised the alarm at the time of Product Backlog Grooming or Sprint Planning meeting and now at the time of EXECUTION (in middle of the sprint)

he says that he is not able to understand the Story (Requirement)

How SM should handle this situation? Because QA guy is mentioning this issue very late and at the point of time when delivery (work) is expected from him.

Did the requirement meet the INVEST criteria for a user story at the time of Sprint Planning, and was it therefore considered to be testable?

Thank you everyone for the response.

Your answers helps me in dealing with 'real life' challenges.

@Ian - Yes, requirement meet the INVEST criteria.