Попробуйте (если вы не хотите использовать библиотеку парсера HTML):
FileReader fileReader = new FileReader(file);
BufferedReader buffRd = new BufferedReader(fileReader);
BufferedWriter out = new BufferedWriter(new FileWriter(newFile.txt));
String s;
int writeTo = 0;
while ((s = br.readLine()) !=null)
{
if(s.contains("<p>"))
{
writeTo = 1;
try
{
out.write(s);
}
catch (IOException e)
{
}
}
if(s.contains("</p>"))
{
writeTo = 0;
try
{
out.write(s);
}
catch (IOException e)
{
}
}
else if(writeTo==1)
{
try
{
out.write(s);
}
catch (IOException e)
{
}
}
}