Segmenting specific targets or biomarkers is necessary to analyze optical coherence tomography angiography (OCTA) images. Previous methods typically segment all the targets in an OCTA sample, such as retinal vessels (RVs). Although these methods perform well in accuracy and precision, OCTA analyses often focusing local information within the images which has not been fulfilled. In this paper, we propose a method called SAM-OCTA for local segmentation in OCTA images. The method fine-tunes a pre-trained segment anything model (SAM) using low-rank adaptation (LoRA) and utilizes prompt points for local RVs, arteries, and veins segmentation in OCTA. To explore the effect and mechanism of prompt points, we set up global and local segmentation modes with two prompt point generation strategies, namely random selection and special annotation. Considering practical usage, we conducted extended experiments with different model scales and analyzed the model performance before and after fine-tuning besides the general segmentation task. From comprehensive experimental results with the OCTA-500 dataset, our SAM-OCTA method has achieved state-of-the-art performance in common OCTA segmentation tasks related to RV and FAZ, and it also performs accurate segmentation of artery-vein and local vessels. The code is available at https://github.com/ShellRedia/SAM-OCTA-extend.