Is this MAC scheme secure?
It is not secure in general, but not insecure in general either.

For example, you can get a MAC algorithm for which it would be secure by concatenating constant data to a secure MAC. $Tag_k(m) = M_k(m)||0^n$ is a secure MAC if $M$ is. And clearly taking the first half of that is a secure MAC if $n = |M_k(m)|$.

On the other hand, reverse the order of the constant and non-constant part above and you get a MAC scheme for which taking the first half is very insecure.

If your secure MAC algorithm is based on a PRF, you can take the first half and have a MAC that is secure, but easier to guess randomly. (Because a secure PRF is a secure MAC and a truncated PRF is still a PRF.) Many MAC algorithms like HMAC and CMAC, for example, can be truncated for this reason.