Clinical assessment of speech abnormalities in Cerebellar Ataxia (CA) is subjective and prone to intra- and inter-clinician inconsistencies. This paper presents an automated objective method based on a single syllable repetition task to detect and quantify speech-timing anomalies in ataxic speech. Such a technique is non-invasive, reliable, fast, cost-effective and can be used in the comfort of home without any professional assistance. A mathematically inclined topographic prominence-based algorithm with an extensive outlier detection mechanism is designed for the automatic detection of syllables in the captured speech data. Six acoustic features and eleven corresponding speech timing and vocal stability measurements were extracted during the topographical prominence analysis. These features are used to classify CA from normal speakers and objectively identify the CA speakers based on their severity. The effectiveness of the proposed algorithm is experimentally evaluated through a clinical study involving 63 patients diagnosed with CA (to varying degrees of dysarthria) and 28 age-matched normal speakers. In syllable detection, our proposed automated algorithm achieved an accuracy of 95.6% and 99.1% for ataxic and normal speech respectively. These speech samples were clinically rated using the Scale for the Assessment and Rating of Ataxia (SARA). SVM classifier achieved a classification accuracy of 84.7% (area under ROC=0.91) in healthy-CA discrimination and 74.7% (average area under ROC=0.82) in the modified 4-level CA severity estimation based on SARA ratings. The strong classification ability of selected features and the SVM model supports suitability of this scheme to monitor speech motor abnormalities in persons suffering from CA.