Developers usually use TPLs to facilitate the development of the projects to avoid reinventing the wheels, however, the vulnerable TPLs indeed cause severe security threats. The majority of existing research only considered whether projects used vulnerable TPLs but neglected whether the vulnerable code of the TPLs was indeed used by the projects, which inevitably results in false positives and further requires additional patching efforts and maintenance costs. To address this, we propose VAScanner, which can effectively identify vulnerable root methods causing vulnerabilities in TPLs and further identify all vulnerable APIs of TPLs used by Java projects. Specifically, we first collect the initial patch methods from the patch commits and extract accurate patch methods by employing a patch-unrelated sifting mechanism, then we further identify the vulnerable root methods for each vulnerability by employing an augmentation mechanism. Based on them, we leverage backward call graph analysis to identify all vulnerable APIs for each vulnerable TPL version and construct a database consisting of 90,749 (2,410,779 with library versions) vulnerable APIs with 1.45% false positive proportion with a 95% CI of [1.31%, 1.59%] from 362 TPLs with 14,775 versions. Our experiments show VAScanner eliminates 5.78% false positives and 2.16% false negatives owing to the proposed sifting and augmentation mechanisms. Besides, it outperforms the state-of-the-art method-level tool in analyzing direct dependencies, Eclipse Steady, achieving more effective detection of vulnerable APIs. Furthermore, in a large-scale analysis of 3,147 projects using vulnerable TPLs, we find only 21.51% of projects (with 1.83% false positive proportion and a 95% CI of [0.71%, 4.61%]) were threatened through vulnerable APIs by vulnerable TPLs, demonstrating that VAScanner can potentially reduce false positives significantly.