You can't do it using the HYPERLINK function but there is an alternative approach.
Insert Link Shortcut
You can put multiple hyperlinks in Google Sheets cells using the "insert link" shortcut:
- PC: CTRL+K
- Mac: CMD+K
Steps
- Select the first word you want to hyperlink.
- Press CTRL+K
- Enter the link URL.
- Repeat the steps above for the next, and subsequent words, you want hyperlinked.
Resource: Keyboard shortcuts for Google Sheets