The reproduction of grapevine genotypes, one of the most important species in the world, while preserving their genetic characteristics, is practically done by rooting cuttings. Adventive rooting of cutting studies for seedling production in nursery conditions often remain below the expected productivity level due to biotic and abiotic stress-related reasons. Studies to increase nursery yields are still on the agenda of grapevine researchers. In this study, the effects of silver nanoparticles (AgNPs) produced by the green synthesis method using grape seed extract and AgNO3 on rooting and vegetative growth of the standard (TS 4027) cuttings taken during the dormancy period of Vitis vinifera L. cvs Ekşi Kara and Gök Üzüm were investigated under greenhouse conditions. Cuttings treated by keeping in 0.1, 0.2 g⋅L−1 AgNPs, 0.1, 0.2 g⋅L−1 IBA aqueous solutions for 24 h were planted in black, 1 L volume seedling bags filled with 1:1 peat: perlite in the greenhouse, while the control was kept in pure water for 24 h and planted. Changes in sprouting rate, plant transformation rate, shoot length, shoot diameter, number of nodes, stomatal conductance, leaf temperature, photosynthetic efficiency, leaf fresh and dry weight, SPAD, root number, root length, root fresh and root weight were examined in developing seedlings. In evaluating the effects of AgNPs and Indole-3-butyric acid (IBA) treatments on cutting rooting and vegetative development, ANOVA, post hoc analysis with the Tukey test, and Principal Component Analyses (PCAs) were used to better understand and depict the correlations between the examined variables. This analysis method was performed using ggplot2 in the R Studio program. The heatmap generated by the pheatmap package was used to visualize the correlation and variation. As a result of this study, AgNPs applications were found to be more effective than IBA treatments in the rooting of grapevine cuttings and the vegetative development of young plants. In conclusion, 0.1 g⋅L−1 AgNPs can be tested as a support and/or economical alternative to IBA for the promotion of rooting of cuttings and vegetative development of young plants for subsequent clonal propagation.