There's no built-in SVM classifier layer available in Deep Network Designer, but you should still be able to use the approach outlined in the referenced paper in MATLAB.
Remove the softmax and classifier layers, so a fully-connected layer is the final layer of the network. Then, use the activations from that layer to train an SVM classifier. Take a look at this example, which covers using a pretrained network as a feature extractor.
Extract the features at the layer of interest (e.g. 'fc8') using the activations function, then use those to train a separate SVM classifier, e.g. with fitcecoc.
% Extract features from 'fc8' layer.
layer = 'fc8';
featuresTrain = activations(net,augimdsTrain,layer,'OutputAs','rows');
% Train SVM classififer with those features.
YTrain = imdsTrain.Labels;
classifier = fitcecoc(featuresTrain,YTrain);
