File parsing code in C++
First off streams and specifically the stream operators >> and &lt;&lt; are designed for robustness not speed. They make the code harder to write incorrectly (and provide some local specific conversions) that make expensive in terms of using (consider changing to C fscanf() if speed is paramount).

So if speed is you objective streams is not the best choice.  

Assuming we are staying with streams (Ask another question about how to write this in C for speed):  

Dead Code

Second delete dead code (it confuses a review) and costs in creation.

    std::string new_line;


Small Inefficiencies

There is no need to create the cell object each time through the loop create it once outside the loop. (Personally I would leave it in the loop, but if you are going for speed then this is an obvious simple save).

When scanning the date you are making a copy of the value:

    std::string my_date = my_str_vec[0];


No need just make a reference (you  can even use a const reference for safety):

    std::string const&amp;   my_date = my_str_vec[0];
          //    ^^^^^^


Use Reserve

Building the string character by character may not be the most efficient way of getting the date (as the string processed_date may be resized on each insert). 

    for(my_iter = my_date.begin(); my_iter != my_date.end(); ++my_iter) {
        if(std::isalnum(*my_iter) || *my_iter == ' ')
            processed_date.append(1,(*my_iter));
    }


Use reserve so you know that it is not re-sized internally, then use a standard algorithm for optimal looping:

processed_date.reserve(my_date.size());  // Note: not resize()
std::remove_copy(my_date.begin(), my_date.end(), 
                 std::back_inserter(processed_date),
                 [](char const&amp; my_char) {return !(std::isalnum(*my_char) || *my_char == ' ');}
                );
// Note if you don't have C++0x then lamda is easily replaced by a functor.


Standard algorithms.

Your code will be optimal when you use the standard algorithms. Its worth learning what is available.

http://www.sgi.com/tech/stl/table_of_contents.html
See section 5

I showed you how to copy all but the characters you want. But there is one to remove all elements in-place. I'll let you experiment.