Lets' break this down. The sentence is reported speech Trump(subject) said(verb) ...(reported speech). The reported speech is backshifted. I'll bring that to the front.
[The U.S.] subject [will begin] verb [[charging additional duties] [of 25 percent] [on $50 billion worth of Chinese imports] [in response to what Trump says is theft of American intellectual property.]]
The verb phrase "will begin" is completed by the gerund "charging additonal duties". There is then a series of prepositional phrases.
The last of these has "in response to (noun phrase)", and the noun phrase uses another clause of reported speech. The pronoun "what" means "the thing that..." and is the complement of "is theft" in the reported speech.
in response to [what Trump says is theft of American intellectual property]
So the duties are in response to (something)
Trump said that (something) is the theft of American IP.
So the duties are in response to the theft of American IP (according to Trump)