What is the result of modifying the reagents in the Sanger method?
If by one of the dideoxynucleotides, you mean one of ddATP, ddCTP, ddGTP, or ddTTP was omitted from the process, then the sequencing would only be able to terminate for the other three dideoxynucleotides. And you would not be able to get the full sequence, and only nucleotides of whatever three you had.

The function of ddNTPs (the dideoxnucleotides) is to stop the elongation of DNA and to subsequently be read by either fluorescence or radioactivity. 

Source: https://en.wikipedia.org/wiki/Sanger_sequencing