1. Wood density is considered a key functional trait influencing the growth and survival of woody plants and has been shown to be related to a slow–fast rate-of-living continuum. Wood density is, however, an emergent trait arising from several vascular properties of wood, including the diameter and frequency of xylem conduits. 2. We aimed to test the hypotheses that there is a set of inter-related trade-offs linked to the different functions of wood, that these trade-offs have direct consequences for tree growth and survival and that these trade-offs underlie the observed correlations between wood density and demographic rates. We evaluated the covariation between xylem anatomical traits among woody species of New Zealand and whether that covariation had the potential to constrain variation in wood density and demographic rates. 3. Several xylem traits were strongly correlated with each other, but wood density was not correlated with any of them. We also found no significant relationships between wood density and growth or mortality rate. Instead, growth was strongly related to xylem traits associated with hydraulic capacity (conduit diameter and a conductivity index) and to maximum height, whereas mortality rate was strongly correlated only with maximum height. The diameter and frequency of conduits exhibited a significant negative relationship, suggesting a trade-off, which restricted variation in wood density and growth rate, but not mortality rate. 4. Our results suggest, for woody species in New Zealand, that growth rate is more closely linked to xylem traits determining hydraulic conductance, rather than wood density. We also found no evidence that denser woods conferred higher survival, or that risk of cavitation caused by wide conduits increased mortality. 5. In summary, we found little support for the idea that wood density is a good proxy for position along a fast–slow rate-of-living continuum. Instead, the strong, negative relationship between vessel diameter and frequency may constrain the realized diversity of demographic niches of tree species in New Zealand. Trade-offs in function therefore have the potential to shape functional diversity and ecology of forest communities by linking selection on structure and function to population-level dynamics.