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We study simultaneous soft ($0.7 - 7$ keV) and hard ($7 - 20$ keV) X-raylight curves at a total of eight epochs during $2016 - 2019$ of two TeV blazarsMrk 421 and 1ES 1959+650 observed by the SXT and LAXPC instruments onboardAstroSat. The light curves are $45 - 450$ ks long and may be sampled with timebins as short as $600 - 800$ sec with high signal to noise ratio. The blazarsshow a harder when brighter trend at all epochs. Discrete cross-correlationfunctions indicate that the hard and soft X-ray variability are stronglycorrelated. The time lag is consistent with zero in some epochs, and indicateshard or soft lag of a few hours in the rest. In the leptonic model of blazaremission, soft lag may be due to slower radiative cooling of lower energyelectrons while hard lag may be caused by gradual acceleration of the highenergy electrons emitting at the hard X-ray band. Assuming the above scenarioand the value of the Doppler factor ($\delta$) to be $10 - 20$, the hard andsoft lags may be used to estimate the magnetic field to be $\sim 0.1$ Gauss andthe acceleration parameter to be $\sim 10^4$ in the emission region. Due to theavailability of the high time resolution ($\sim$ minutes to hours) light curvesfrom AstroSat, the value of the illusive acceleration parameter could beestimated, which provides a stringent constraint on the theories of particleacceleration in blazar jets.

Correlated Short-Timescale Hard-Soft X-ray Variability of the Blazars Mrk 421 and 1ES 1959+650 using $\textit{AstroSat}$