We introduce a novel framework for learning vector representations of tree-structured geometric data focusing on 3D vascular networks. Our approach employs two sequentially trained Transformer-based autoencoders. In the first stage, the Vessel Autoencoder captures continuous geometric details of individual vessel segments by learning embeddings from sampled points along each curve. In the second stage, the Vessel Tree Autoencoder encodes the topology of the vascular network as a single vector representation, leveraging the segment-level embeddings from the first model. A recursive decoding process ensures that the reconstructed topology is a valid tree structure. Compared to 3D convolutional models, this proposed approach substantially lowers GPU memory requirements, facilitating large-scale training. Experimental results on a 2D synthetic tree dataset and a 3D coronary artery dataset demonstrate superior reconstruction fidelity, accurate topology preservation, and realistic interpolations in latent space. Our scalable framework, named VeTTA, offers precise, flexible, and topologically consistent modeling of anatomical tree structures in medical imaging.