Sawbill means: A British colloquial name for the red-breasted merganser , a diving duck with a serrated bill adapted for gripping fish. The 'saw' in the name refers directly to the tooth-like serrations along the. There is no real cause for parental concern; it is descriptive vocabulary rather than risky behaviour. If your teen uses it, context will usually make the intent clear. A short, curious question about where they heard it is usually all that is needed to know whether to follow up.