Why I have an exception when create regex object in VS2015?

Your exception doesn't happen when building the regex but when you throw your own.

First you are checking that your string is exactly 10 characters long. If you put a string of size 10 in your string everything works as it should:

int main()
{
    std::string str = "20151107AB";
    int year = 0;
    int month = 0;
    int day= 0;

    if (str.size() != 10)
        throw std::exception("not a date");

    std::regex regEx("^[0-9]{4}[0-9]{2}[0-9]{2}");
    std::regex delims("([^.,;-]+)");

    std::smatch match;
    if (std::regex_match(str.cbegin(), str.cend(), match, regEx)) {
        std::stringstream ss;
        std::string tmp(match.str());
        std::copy(std::sregex_token_iterator(tmp.cbegin(), tmp.cend(), delims, -1),
            std::sregex_token_iterator(),
            std::ostream_iterator<std::string>(ss, "\n"));
        ss >> year;
        ss >> month;
        ss >> day;
    }
} 

If you remove the "AB" you'll get the error as described in your question.

int main()
{
    std::string str = "20151107";
    int year = 0;
    int month = 0;
    int day= 0;

    if (str.size() != 10)
        throw std::exception("not a date");

    std::regex regEx("^[0-9]{4}[0-9]{2}[0-9]{2}");
    std::regex delims("([^.,;-]+)");

    std::smatch match;
    if (std::regex_match(str.cbegin(), str.cend(), match, regEx)) {
        std::stringstream ss;
        std::string tmp(match.str());
        std::copy(std::sregex_token_iterator(tmp.cbegin(), tmp.cend(), delims, -1),
            std::sregex_token_iterator(),
            std::ostream_iterator<std::string>(ss, "\n"));
        ss >> year;
        ss >> month;
        ss >> day;
    }
}

If you now remove the length-check everything is working as it should again.

int main()
{
    std::string str = "20151107";
    int year = 0;
    int month = 0;
    int day= 0;

    std::regex regEx("^[0-9]{4}[0-9]{2}[0-9]{2}");
    std::regex delims("([^.,;-]+)");

    std::smatch match;
    if (std::regex_match(str.cbegin(), str.cend(), match, regEx)) {
        std::stringstream ss;
        std::string tmp(match.str());
        std::copy(std::sregex_token_iterator(tmp.cbegin(), tmp.cend(), delims, -1),
            std::sregex_token_iterator(),
            std::ostream_iterator<std::string>(ss, "\n"));
        ss >> year;
        ss >> month;
        ss >> day;
    }
}

Also, if you catch the exception everything is still fine (yet the code isn't executed)

int main()
{
    try
    {
        std::string str = "20151107";
        int year = 0;
        int month = 0;
        int day = 0;

        if (str.size() != 10)
            throw std::exception("not a date");

        std::regex regEx("^[0-9]{4}[0-9]{2}[0-9]{2}");
        std::regex delims("([^.,;-]+)");

        std::smatch match;
        if (std::regex_match(str.cbegin(), str.cend(), match, regEx)) {
            std::stringstream ss;
            std::string tmp(match.str());
            std::copy(std::sregex_token_iterator(tmp.cbegin(), tmp.cend(), delims, -1),
                std::sregex_token_iterator(),
                std::ostream_iterator<std::string>(ss, "\n"));
            ss >> year;
            ss >> month;
            ss >> day;
        }
    }
    catch (std::exception& e)
    {
        //handle
    }
}

So my assumption on this is that you don't catch the exception anywhere, which might cause memory corruption as the standard doesn't define whether that stack must be unwound in this case.

I would recommend to 1. read Does it make sense to catch exceptions in the main(...)? 2. correctly catch the exception thrown by Date::operator=

Maybe you also want to install a global exception handler (to safely shutdown your program).

And one other thing: Why do you check the length of your date string being exactly 10, when you only need 8 characters?