Dissipative solitons generated in normal-dispersion mode-locked lasers are stable localized coherent structures with a mostly linear frequency modulation (chirp). The soliton energy in fiber lasers is limited by the Raman effect, but implementation of the intracavity feedback at the Stokes-shifted wavelength enables synchronous generation of a coherent Raman dissipative soliton. Here we demonstrate a new approach for generating chirped pulses at new wavelengths by mixing in a highly-nonlinear fiber of these two frequency-shifted dissipative solitons, as well as cascaded generation of their clones forming in the spectral domain a comb of highly chirped pulses. We observed up to eight equidistant components in the interval of more than 300 nm, which demonstrate compressibility from ∼10 ps to ∼300 fs. This approach, being different from traditional frequency combs, can inspire new developments in fundamental science and applications such as few-cycle/arbitrary-waveform pulse synthesis, comb spectroscopy, coherent communications and bio-imaging.