can I use t-sne or PCA to reduce number of classes? I wanted to know if I can use t-sne or PCA to reduce the number of classes depending on the similarity between them. For example, if I have 100  classes of 100 different animals and would like to put all the cats in a group and all the dogs in a group etc. (to get few groups of these 100 classes).
No. t-Distributed Stochastic Neighbor Embedding (t-SNE) and Principal Component Analysis (PCA) are dimension reduction techniques, aka fewer columns of a tidy dataframe. 

Clustering will reduce the number of observations, aka fewer rows of a tidy dataframe. In particular, you might be looking for hierarchical clustering.