Previous works for achieving mechanical squeezing focused mainly on the sole squeezing manipulation method. Here we study how to construct strong steady-state mechanical squeezing via the joint effect between Duffing nonlinearity and parametric pump driving. We find that the 3 dB limit of strong mechanical squeezing can be easily overcome from the joint effect of two different below 3 dB squeezing components induced by Duffing nonlinearity and parametric pump driving, respectively, without the need of any extra technologies, such as quantum measurement or quantum feedback. Especially, we first demonstrate that, in the ideal mechanical bath, the joint squeezing effect just is the superposition of the two respective independent squeezing components. The mechanical squeezing constructed by the joint effect is fairly robust against the mechanical thermal noise. Moreover, different from previous mechanical squeezing detection schemes, which need to introduce an additional ancillary cavity mode, the joint mechanical squeezing effect in the present scheme can be directly measured by homodyning the output field of the cavity with an appropriate phase. The joint idea opens up a new approach to construct strong mechanical squeezing and can be generalized to realize other strong macroscopic quantum effects.