If I have the right to remain silent, do I also have the right to refuse giving my DNA away? IANAL but if I have the right to not speak so as to not incriminate myself, why wouldn't I also have the right to not have my blood drawn (or mucus swabbed) so as to not incriminate myself?
I don't live in New York but, I'm often there. If an officer there wanted to take a sample of my DNA for an offense such as speeding, I'd refuse. If he persisted, I'd try to invoke Miranda Rights. If he persisted after that, I'd fight back as he tried to take the sample, recover for a few months in the hospital after he beat me senseless and then sue for police brutality. Essentially, that's what it's going to take to get this law overturned if it gets passed.
How do ignorant comments like this get modded up to +5?
First of all, since you describe an offense involving driving, you should know that the implied consent laws passed by the states requires that you give consent to brethalyzer, etc. It'd be trivial for the legislatures to add a DNA sample to the list. You can still refuse, but you'll lose your license.
Second, the Supreme Court has held that the Fifth Amendment only applies to testimonial evidence. In Schmerber v. California, 384 U.S. 757 (1966), the Supreme Court held that extracting blood against the suspect's will was permissible: "On the other hand, both federal and state courts have usually held that it offers no protection against compulsion to submit to fingerprinting, photographing, or measurements, to write or speak for identification, to appear in court, to stand, to assume a stance, to walk, or to make a particular gesture. . . . Not even a shadow of testimonial compulsion upon or enforced communication by the accused was involved either in the extraction or in the chemical analysis. Petitioner's testimonial capacities were in no way implicated; indeed, his participation, except as a donor, was irrelevant to the results of the test, which depend on chemical analysis and on that alone. Since the blood test evidence, although an incriminating product of compulsion, was neither petitioner's testimony nor evidence relating to some communicative act or writing by the petitioner, it was not inadmissible on privilege grounds."
More recently, Doe v. United States, 487 U.S. 201 (1988) cites Schmerber and others:
An examination of the Court's application of these [487 U.S. 201, 210] principles in other cases indicates the Court's recognition that, in order to be testimonial, an accused's communication must itself, explicitly or implicitly, relate a factual assertion or disclose information. 9 Only then is a person compelled to be a "witness" against himself.
This understanding is perhaps most clearly revealed in those cases in which the Court has held that certain acts, though incriminating, are not within the privilege. Thus, a suspect may be compelled to furnish a blood sample, Schmerber v. California, 384 U.S., at 765 ; to provide a handwriting exemplar, Gilbert v. California, 388 U.S., at 266 -267, or a voice exemplar, United States v. Dionisio, 410 U.S. 1, 7 (1973); to stand in a lineup, United States v. Wade, 388 U.S., at 221 -222; and to wear particular clothing, Holt v. United States, 218 U.S. 245, 252 -253 (1910). These decisions are grounded on the proposition that "the privilege protects an accused only from being compelled to testify against himself, or otherwise provide the State with evidence of a testimonial or communicative nature." Schmerber, 384 U.S., at 761 . The Court accordingly held that the privilege [487 U.S. 201, 211] was not implicated in each of those cases, because the suspect was not required "to disclose any knowledge he might have," or "to speak his guilt," Wade, 388 U.S., at 222 -223. See Dionisio, 410 U.S., at 7 ; Gilbert, 388 U.S., at 266 -267. It is the "extortion of information from the accused," Couch v. United States, 409 U.S., at 328 , the attempt to force him "to disclose the contents of his own mind," Curcio v. United States, 354 U.S. 118, 128 (1957), that implicates the Self-Incrimination Clause. See also Kastigar v. United States, 406 U.S. 441, 445 (1972) (the privilege "protects against any disclosures that the witness reasonably believes could be used in a criminal prosecution or could lead to other evidence that might be so used") (emphasis added). "Unless some attempt is made to secure a communication - written, oral or otherwise - upon which reliance is to be placed as involving [the accused's] consciousness of the facts and the operations of his mind in expressing it, the demand made upon him is not a testimonial one." 8 Wigmore 2265, p. 386. 10 [487 U.S. 201, 212]
So no, the Fifth Amendment doesn't mean they can't collect a DNA sample.
Finally, if you "fight back" as the officer tries to collect evidence, and if you live through the experience, you're not going to win a brutality suit--you don't have the right to resist an officer in the lawful performance of his duties.