Yes, you can do that in JavaScript:
var str = "áéíóú";
var result = str.replace(/[áéíóú]/g, function(m) {
    switch (m) {
        case "á":
            return "a";
        case "é":
            return "e";
        case "í":
            return "i";
        case "ó":
            return "o";
        case "ú":
            return "u";
    }
});
Another way is a lookup table:
var replacements = {
    "á": "a",
    "é": "e",
    "í": "i",
    "ó": "o",
    "ú": "u"
};
var str = "áéíóú";
var result = str.replace(/[áéíóú]/g, function(m) {
    return replacements[m];
});
Those work because replace can accept a regular expression, and the "replacement" can be a function. The function receives the string that matched as an argument. If the function doesn't return anything, or returns undefined, the original is kept; if it returns something else, that's used instead. The regular expression /[áéíóú]/g is a "character" class meaning "any of these characters", and the g at the end means "global" (the entire string).