multiplication of two 14bits number

unless you have some special application, then in the perspective of signal processing I would avoid saturation altogether or so since it leads to nonlinearity. However in practice you might consider an occasional clipping if you get the advantage of one extra bit of resolution.

In particular for discardind one MSB: to multiply two14 bit signed numbers then the maximum positive result is going to be:

-2^13 * -2^13 = 2^26 i.e. 1 one short of 27 bits

in other words n bits * n bits requires 2n bits only for the sake of one single case of -2^n-1 * -2^n-1.

The conclusion is that you can discard 1 MSB with added clipping and discard 13 LSBs. The doubling of gain is the side effect but resolution is maintained. Doing so, you are also forcing partially symmetric swing.

In some other cases, maximum expected values may even allow you discarding more MSBs e.g. when multiplying sin * cos