something wrong with my loop where array (String type) where each word is written, if not repeated in a loop, is written to a dynamic array

Add the value from mas, only if the inner-loop does not find a match.

boolean b;
arr.add(mas[0]);
for(int i=1;i<mas.length;i++) {
    b = false;
    for(int j=0;j<arr.size();j++)
        if(mas[i].equals(arr.get(j))||mas[i].equals("")){
            b = true;
            break;
        }
    if (!b) arr.add(mas[i]);
}
for(int j=0;j<arr.size();j++) {
    System.out.print(arr.get(j)+";");
}

Output

car;cycle;bomj;

Ideally, just use the List#contains method.
And, utilize the String#join method to print the concatenated values.

String s;
arr.add(mas[0]);
for(int i=1;i<mas.length;i++)
    if (!arr.contains(s = mas[i])) arr.add(s);
System.out.println(String.join(";", arr));

Output

car;cycle;bomj

If I have interpreted good your problem, you should add the item in the list only after the second loop.

arr.add(mas[0]);
outer: for(int i=1;i<mas.length;i++) {
    if ("".equals(mas[i])) {
        continue;
    }
    for(int j=0;j<arr.size();j++) {
        if(mas[i].equals(arr.get(j))){
                break outer;
            }
        }
        arr.add(mas[i]);
    }
    for(int j=0;j<arr.size();j++) { 
        System.out.print(arr.get(j)+";");
    }

I have edited the answer adding a label on the outer loop named "outer" and made some minor changes to make it more readable.

    arr.add(mas[0]);    
    int raz=0;
    for(String word : mas ) {
        raz=0;
        for(int j=0;j<arr.size();j++) {
            if(word.equals(arr.get(j))||word.equals("")){
                raz--;
                break;
            }
            raz++;
        }
        if(raz==arr.size()){
            arr.add(word);
        }
    }