This election cycle saw the introduction of Jeb Bush, Marco Rubio and even Ted Cruz in the Republican primaries; the Republican establishment has been attempting to court more Hispanic voters in the face of an overall declining White population and voter base. Why then, would Trump attempt to further hammer the prevailing political strategy of his own party?
First, it is a low-risk move because Martinez appears to be a low-key establishment figure and also not a nationally-recognized leader. Any attack upon her is therefore a relatively safe one because Martinez does not appear to be highly networked; her entire career has been spent in or around New Mexico. Any attack on Martinez is also an attack on the political establishment which the Republican base is now love to loathe. Moreover, Hispanic voters lean generally towards the Democratic Party. Thus, Donald Trump is probably correct in estimating that unless the Republican leadership intends to adopt more left-leaning policies (e.g. more immigration benefits like legalization of illegal immigrants), any attempt to court Hispanic voters with "compassionate" candidates like Jeb Bush or figureheads such as Marco Rubio will fail for want of substantive appeal, and so there is really no love lost in attacking a Hispanic leader like Martinez.
Second, Trump's attack highlights his credibility with his core constituency of anti-establishment, primarily White voters. It indirectly links the New Mexican Governor, who is of Mexican descent, with (New) Mexicans who are perceived to be on the dole; the key word "Mexican" is rung over and over just by this simple move. His attack, in one swoop, hits on his highlighted themes of immigration, his proposed wall on the Mexican border, entitlement reform, and the lackadaisical efforts by the Republican establishment to address these issues.
Third, Martinez is boxed in and cannot fight back. Martinez cannot deny Trump's factual claim about entitlement growth, cannot deny that entitlement reform is a big focus of the Republican voter base, and in any case, fighting back against the crown prince of the Republican Party is dangerous for Martinez's own political health. So Martinez's best response is a non-response -- "The governor will not be bullied into supporting a candidate until she is convinced that candidate will fight for New Mexicans,” said Mike Lonergan, Ms. Martinez’s press secretary. “Governor Martinez doesn’t care about what Donald Trump says about her.”
Fourth, with this one unorthodox move, Trump has also continued to grab the media's attention, giving himself more free exposure.
Then, for the coup-de-grace: Trump extends an olive branch to Martinez, saying that he has "always liked" her and now wants to meet with her.
Martinez is once again forced into dancing to Trump's tune. Trump made Martinez an offer she cannot refuse. If Martinez rejects Trump's overtures, Martinez will be seen as a someone who cannot stand criticism and a sore loser, will lose out in favors from a potential Trump administration, as well as opening herself up to challengers for her own future elections. Martinez could either join Trump and ride on the new wave of Republican grassroots popularism, or jump on the sinking ship that Mitt Romney and other establishment "loser" figures have since consigned themselves to.
Martinez, therefore, can only accept Trump's offer, pretend to seriously discuss matters with Trump, and like true Republican heavy hitters Reince Priebus and Paul Ryan, will ultimately fall in line behind Trump. You can count on it.