Machine learning (ML) and Deep Neural Networks (DNN) have greatly aided the problem of Automatic Speech Recognition (ASR). However, accurate ASR for dysarthric speech remains a serious challenge. The dearth of usable data remains a problem in applying ML and DNN techniques for dysarthric speech recognition. In the current research, we address this challenge using a novel two-stage data augmentation scheme, a combination of static and dynamic data augmentation techniques, designed by leveraging an understanding of the characteristics of dysarthric speech. We explore speaker-independent ASR using modifications to healthy speech using various perturbations, devoicing of consonants, and voice conversion, comprising stage one or static augmentations. Subsequent to the first stage, a modified SpecAugment algorithm tailored for dysarthric speech is employed. This variant, termed Dysarthric SpecAugment, leverages the characteristics of dysarthric speech and forms the second stage of the two-stage augmentation approach. This acoustic model is used to pre-train a speaker-dependent ASR using dysarthric speech. The objective of this work is to improve the ASR performance for dysarthric speech using the two-stage data augmentation scheme. An end-to-end ASR using a Transformer acoustic model is used to evaluate the data augmentation scheme on speech from the UA dysarthric speech corpus. We achieve an absolute improvement of 10.7% and a relative improvement of 29.2% in word error rate (WER) over a baseline with no augmentation, with a final WER of 25.9% for the speaker-dependent system.