The genus Spiraea is well represented in the Russian flora. Several phytochemical and bioactivity studies, completed so far with several individual species of this genus, indicate young Spiraea shoots as a promising source of pharmaceutically and nutraceutically active natural products. Therefore, a broad-scale phytochemical analysis of shoot extracts from multiple Russian Spiraea species (i.e., profiling of secondary metabolites and assignment of their structures), complemented with comprehensive activity screening, might give access to valuable information on the structure–activity relationship (SAR) of their constituents. However, despite a lot of phytochemical and bioactivity information on individual species being available, these data are mostly fragmentary and do not allow for building a general picture, and in-depth comprehensive studies are still missing. Therefore, to fill this gap, here, we present a comprehensive metabolite profiling study accomplished with 15 of the most widely spread Russian Spiraea species, which was complemented with appropriate bioactivity screening of their first-year shoot alcoholic extracts. A chromatography–mass spectrometric (LC-MS) analysis revealed 33 major constituents of the shoot isolates, which were dominated by flavonoids (quercetin and kaempferol derivatives) and hydroxycinnamic acids (caffeic, ferulic, and coumaric acid derivatives). Their relative quantification indicated that most of the identified major components were distributed among all of the studied extracts with minimal overlap in their composition and relative abundance. The antioxidant activity screening revealed the high efficiency of all of the extracts as potential redox protectors, acting at the levels of radical scavenging (DPPH assay) and quenching cation radicals (TEAC assay) and superoxide anion radicals (NBT assay). Screening the antiviral and antimicrobial activity of the same extracts revealed significant antiviral activity at a concentration of 2 µg/mL, and high (MIC < 1 mg/mL) or moderate (1 mg/mL ≤ MIC ≤ 4 mg/mL) antibacterial activity against Gram-positive and Gram-negative strains. The structures responsible for the manifestation of the studied types of activity were tentatively assigned using a bioinformatics-based strategy. This analysis revealed the most bioactive Spiraea species that might be promising for further in-depth phytochemical analysis and evaluations of their structure–activity relationships (SARs). In this context, we consider S. humilis, which simultaneously showed antioxidant, antimicrobial, and antiviral activity; S. media, with marked antioxidant, antimicrobial, and cytotoxic properties; S. ussuriensis, a strong antioxidant and cytotoxic species; and S. trilobata, with a combination of antioxidant and antiviral properties.