It's probably an infringement of the rightsholder of the "Toy Story" franchise. You're best off getting permission from the owner of the film to use and alter their clips in your song. If you can't get permission, you're best of editing the film clips out of your song.
Even a song called "Buzz Lightyear" that doesn't borrow clips from the "Toy Story" franchise might need permission. It's arguable that you'd need to be careful about your song being considered a "fair use," and not confusing to consumers who might think you and your song were affiliated with the film rightsholders or that they endorsed your song, or that your song unfairly competes with the film and it's ancillary merchandise, but to me it seems unlikely that any of those claims would stick, though they're not impossible.
Disclaimer: Please note that this answer does not constitute legal advice, and should not be relied on, since each state has different laws, each situation is fact specific, and it is impossible to evaluate a legal problem without a comprehensive consultation and review of all the facts and documents at issue. This answer does not create an attorney-client relationship.
To me, the answer is clearly "no" it would not be legal -- especially considering the fact that you created the song "using clips from the movie Toy Story." Those portions of the movie are copyright protected. Even if the clips you've copied consist of dialogue and not music you have nonetheless "sampled" from the movie for which a license to use is very likely required (there have been many, many court decisions addressing "sampling.").
Moreover, as noted by Ms. Koslyn, the name of your song is likely problematic in its own right because it may cause consumers to believe that the copyright / trademark owner of the Toy Story franchise either created your song or endorses, sponsors, or is affiliated with you or your company.
Note: Our First Amendment right of "free" speech does NOT include the right to cash in on the coat tails of others who, through very significant efforts, creatively and successfully exercised their right of free speech. In short, while the public certainly has, in some circumstances, the absolute right to freely use others' copyrighted works, those circumstances do not include, in my opinion, offering your song to the public.
But maybe so. If your song is a parody of the Toy Story movie then maybe your use of Disney's copyrighted material and "Buzz Lightyear" trademark is lawful. Know this: Disney will not think it's lawful and you will very likely receive a cease and desist letter. So before you tweak that bear's nose, you NEED to have an intellectual property attorney review the situation and provide you with advice.