A novel technique for improving the dynamic range of slope-assisted Brillouin optical time domain analysis (SA-BOTDA) is proposed. By modulating the pump pulse with a specially designed signal generated using an arbitrary waveform generator, we may manipulate the shape of Brillouin gain spectrum (BGS) to obtain an enlarged strain dynamic range without increasing significant cost on system complexity. In simulation, we realize a 4.8-times improvement by using a 2-tone signal for pump pulse modulation. In experiment, we modulate a 25-ns-width pump pulse with a 2-tone signal whose frequencies are 43 MHz and 86 MHz respectively and achieve a 100-MHz linear slope span, which is about 4.35 times of that in conventional SA-BOTDA technique. Besides, the BGS manipulation technique realizes an efficient utilization of pump power and only introduces a pump power penalty of 3.53 dB, which allows a promising dynamic strain measurement. In the experiment, we successfully measured a sinusoidal strain signal exerted on a 3-m fiber, with a range from -75 με to 875 με and a frequency of 80 Hz. The measured result shows that the suppression ratio of 2nd-order harmonic is 39.35 dB, and the strain measurement accuracy is 5.26 με. The results indicate that the proposed technique has a desirable performance on dynamic strain measurement.