We derive the asymptotic distribution of the total length $L_{n}$ of a $\operatorname{Beta}(2-\alpha,\alpha)$-coalescent tree for $1<\alpha<2$, starting from $n$ individuals. There are two regimes: If $\alpha\le\frac{1}{2}(1+\sqrt{5})$, then $L_{n}$ suitably rescaled has a stable limit distribution of index $\alpha$. Otherwise $L_{n}$ just has to be shifted by a constant (depending on $n$) to get convergence to a nondegenerate limit distribution. As a consequence, we obtain the limit distribution of the number $S_{n}$ of segregation sites. These are points (mutations), which are placed on the tree’s branches according to a Poisson point process with constant rate.