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Understanding the fundamental charge carrier dynamics is of great significance for photodetectors with both high speed and high responsivity. Devices based on two-dimensional (2D) transition metal dichalcogenides can exhibit picosecond photoresponse speed. However, 2D materials naturally have low absorption, and when increasing thickness to gain higher responsivity, the response time usually slows to nanoseconds, limiting their photodetection performance. Here, by taking time-resolved photocurrent measurements, we demonstrated that graphene/MoTe2 van der Waals heterojunctions realize a fast 10 ps photoresponse time owing to the reduced average photocurrent drift time in the heterojunction, which is fundamentally distinct from traditional Dirac semimetal photodetectors such as graphene or Cd3As2 and implies a photodetection bandwidth as wide as 100 GHz. Furthermore, we found that an additional charge carrier transport channel provided by graphene can effectively decrease the photocurrent recombination loss to the entire device, preserving a high responsivity in the near-infrared region. Our study provides a deeper understanding of the ultrafast electrical response in van der Waals heterojunctions and offers a promising approach for the realization of photodetectors with both high responsivity and ultrafast electrical response.