New York, Oct 24. The Tribune' letter from the city of Mexico on the lStli says : The strugglo between Republic and Empire is fsst draw ing to its eloso. Numerous . ties of guerrillas ha.ve boen reached and j routed. Fresquera, in Sonora, with 8,ÜOÜ men, h.s been driven out by the natives, and by a Mexioan General, without even the interference of the Frene! . Official news represnts him as having left the State and souht for shelter in Arizona. Negrete, with hts pretended army of 5,000 mea, olosely purgned by Gen. Bimconrt, has left thó State of Coahuila, disbanded his troops, and destroved bis Mtülery and ammunitioo.- Heissaidto be now at El Paso with Juárez. His dofcat and withdrawal makes the State of Chihuahua frea, from the Rio Florida up to Sonora. Gen. Fizueraa, who, according to last news, had control of over one huudred miles of country in the State of Oajaca, had been defeated by Gapt. Arrango, with the assistance of the population of the mountains. In this áffair the Juárez leader lost nearly a third of his band, composedof300 ineu, and all his arma and nmniunition. In the State of Queretnro, Tragoso and Martínez have also been beateo, and are iu full retroat, the secretary of the latter having been taken prisoner. It has been disoovered that Martínez received his advices, munitions and money from the city of Mexico, [n whatever place guerrillas haveshown themselves, they have been met either by the French or by the inhabitants and completely routed.